Please help, need to find f^-1 (x)

Please Help, Need To Find F^-1 (x)

Answers

Answer 1

The inverse function [tex]f^{-1}(x)[/tex] is such that

[tex]f\left(f^{-1}(x)\right) = x[/tex]

Plugging [tex]f^{-1}(x)[/tex] into [tex]f(x)[/tex] gives us

[tex]f\left(f^{-1}(x)\right) = \dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x[/tex]

Solve for [tex]f^{-1}(x)[/tex] :

[tex]\dfrac{3f^{-1}(x) + 3}{5f^{-1}(x) + 6} = x \\\\ 3f^{-1}(x)+3=x\left(5f^{-1}(x)+6\right) \\\\ 3f^{-1}(x) + 3 = 5x f^{-1}(x)+6x \\\\ 5xf^{-1}(x)-3f^{-1}(x) = 3 - 6x \\\\ (5x-3)f^{-1}(x)=3-6x \\\\ \boxed{f^{-1}(x)=\dfrac{3-6x}{5x-3}}[/tex]


Related Questions

HELP?h?e?l?pppppppppppppppppppppp

Answers

Answer:

Yes

Step-by-step explanation:

Whats his mistake and the correct awnser

Answers

Answer:

θ ≈ 35.7°

Step-by-step explanation:

His mistake was in using the wrong trig. ratio

Instead of using cosine he should have used the sine ratio

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then

θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )

|7-4x|>1 como se resuelve está inecuación con valor absoluto??

Answers

Answer:

Step-by-step explanation:

te da x<3/2 y x<2, pero la segunda solucion abarca la primera. Por lo tanto creo q seria x<2

Complete the statements for the graph of f(x)=|x|.
The domain of the function is
______________
The range of the function is
______________
The graph is ____ over the interval (0,♾)

The graph is ____ over the interval (♾,0)

Answers

below

Step-by-step explanation:

all real numbers

[0,∞]

increasing

decreasing

Please help!! Thank you!

Answers

Answer:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Step-by-step explanation:

This question is asking for the function's end behavior. An even degree power function with a negative leading coefficient forms a parabola concave down. This means, its vertex represents the maximum and the parabola opens downward (towards negative infinity).

Thus,

[tex]\lim_{x\rightarrow \infty}f(x)=-\infty,\\\lim_{x\rightarrow-\infty}f(x)=-\infty[/tex]

This corresponds with the first answer choice listed:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

find the value of x

Answers

4x - 7 = 3x + 9

x = 16

they're equal because they are opposites by the vertex.

hope it helps :)

Fine FG , given that line HF is perpendicular bisector or EG

Answers

Answer:

FG = 7

Step-by-step explanation:

We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:

EF = 7

EH = 3

HF =?

EF² = EH² + HF²

7² = 3² + HF²

49 = 9 + HF²

Collect like terms

49 – 9 = HF²

40 = HF²

Take the square root of both side

HF = √40

Finally, we shall determine FG. This can be obtained as follow:

GH = 3

HF = √40

FG =.?

FG² = GH² + HF²

FG² = 3² + (√40)²

FG² = 9 + 40

FG² = 49

Take the square root of both side

FG = √49

FG = 7

Choose the correct simplification of the expression b5 ⋅ b4.

b
b9
b20
b−1

Answers

Answer:

b20

Step-by-step explanation:

The blue dot is at what value on the number line?

Answers

Answer:

[tex]8[/tex]

Step-by-step explanation:

Hope it helps you:D

*copied*

Answer:

"8"

4,6,8

Step-by-step explanation:

If p =(3x+1) and q = ( 3x-1),show that : pq+1 =x2

Answers

Answer:

See explanation

Step-by-step explanation:

It should be 9x² not x²

p = (3x + 1) and q = (3x - 1)

pq + 1 = (3x + 1)(3x - 1) + 1

= (9x² - 3x + 3x - 1) + 1

= (9x² - 1) + 1

= 9x² - 1 + 1

= 9x²

Therefore,

pq + 1 = 9x²

Solve: f(x) = (x + 1)(x + 1)

Answers

Answer:

f(x) = x² + 2x + 1

Step-by-step explanation:

you know how to multiply 2 expressions ?

let's say in general we have

(a + b)(c + d)

you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).

so, we get for this simple generic example

a×c + b×c + a×d + b×d

now we use that understanding for our question here.

(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1

A bat and a ball cost 1.10$ in total. The bat costs 1 dollar more than the ball. How much does the ball cost?

Answers

Answer:

$0.5

Step-by-step explanation:

A + B = 1.10

A=1 +B

now A + B = 1.10

A - B = 1 (B cancels out)

2A = 2.10

A= 1.05

A + B = 1.10

substitute A value

1.05 + B = 1.10

B= 1.10-1.05

B=$ 0.5

I believe it’s $0.10

When a boy stands on the bank of a river and looks across to the other bank, the angle of depression is 12°. If he climbs to the top of a 10 ft tree and looks across to other bank, the angle of depression is 15°. What is the distance from the first position of the boy to the other bank of the river? How wide is the river? Give your answers to the nearest foot.

Answers

Please look at the scanned picture.

Which of the integers shown is the greatest?

Answers

Answer:

-3

Step-by-step explanation:

because as you vo more to the negative side the less.it gets and more to the positive side it gets moe

Which equation represents a line that passes through ( -2 , 4 ) and has the slope of 2/5

Answers

Answer:

y = 2/5x +24/5

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

y = 2/5x +24/5

3/z when z=2 SORRY FOR HAVING 2 QUESTIONS IN A ROW

Answers

3/z when z = 2

= 3/2

= 1.5

This is the answer

Answer:

[tex]3/z\: when\:z=2[/tex]

[tex]\frac{3}{z}=2[/tex]

[tex]\frac{3}{z}z=2z[/tex]

[tex]2z=3[/tex]

[tex]\frac{2z}{2}=\frac{3}{2}=z=\frac{3}{2}[/tex]

[tex]z=1.5\right[/tex]

OAmalOHopeO

pls answer fast i need help

Answers

Do it by your self  ok ???


Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If x+2 is a factor of x^3-6x^2-11x+k then k=

Answers

Answer:

k=10

Step-by-step explanation:

Brainliest please~

Answer:

K=10

Step-by-step explanation:

Correct on Plato

Part B
Question
Type the correct answer in the box.
The y-intercept of the parent function, f(x), is
I
The y-intercept of the child function, g(x), is

Answers

Answer:

The y-intercept of the parent function, f(x), is 0

The y-intercept of the child function, g(x), is  7

Step-by-step explanation:

Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.

The solution is :

Vertex is (-2, 0)

y-intercept is 4.

What is vertex?

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

here, we have,

to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':

f(x) = (x+2)^2 = x2 + 4x + 4

Then, to find the vertex, we can use the formula:

x_v = -b / 2a

x_v = -4 / 2 = -2

Now, finding the y_vertex, we have:

f(x_v) = (-2)^2 + 4*(-2) + 4 = 0

So the vertex is (-2, 0)

To find the y-intercept, we make x = 0 and then find f(x):

f(0) = 0 + 0 + 4 = 4

So the y-intercept is 4.

To learn more on vertex click:

brainly.com/question/12563262

#SPJ2

complete question:

Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².

vertex: ( ? , ? )

y-intercept: ?

No idea how to do

[tex]\frac{4r + 20}{r + 5}[/tex]

when r ≠ 5 ?

Answers

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Help!! Please! appreciate it !!

Answers

Answer:

I'm pretty sure you are intended to pick AAS.

Step-by-step explanation:

As it stands, AAS. But this can be an unreliable theorem. If you show that the third angles are equal (which they are) using the fact that if two angles of a triangle are equal to the corresponding angles of another triangle, then the third angle is as well. That means that you can use the much more reliable ASA.

Algebra is hard for me

Answers

Answer: Third Choice. 9

Step-by-step explanation:

Concept:

Here, we need to understand the idea of evaluation.    

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given

4x + 2y -1

x = 3, y = -1

Substitute the value of x and y

4(3) + 2(-1) - 1

Simplify by multiplication

12 - 2 - 1

Simplify by subtraction

9

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Hello!

4x= 4*3 = 12

2y = 2*-1 = -2

12-2  -1= 9

find area of shaded region by using formula a^2-b^2.​

Answers

Answer:

216 cm^2

Step-by-step explanation:

15^2 -3^2 = 225 -9

= 216

Which table shows a proportional relationship between a and b?

Answers

Answer:

It is c

Step-by-step explanation:


use a double angle or half angle identity to find the exact value of each expression

Answers

θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means

cos²(θ) + sin²(θ) = 1   ==>   sin(θ) = -√[1 - cos²(θ)] = -3/5

Now recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ)

==>   sin(2θ) = 2 (-3/5) (4/5) = -24/25

Given sin
=
=
V23 and tan o
find cos 0.
23
11 )
12
?
COS 0 =
TO

Answers

Answer: [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Use trigonometry (shown in image below) to find the 3 side-lengths:

The side opposite of θ = [tex]\sqrt{23}[/tex]The base side adjacent to θ = 11The hypotenuse = 12

According to right triangle trigonometry:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Substitute in the values:

cos θ = [tex]\frac{11}{12}[/tex]

N is the centroid of the triangle. Find XN if XG = 33

Answers

Answer:

XN = 22

Step-by-step explanation:

Recall: the Centroid theorem states that the Centroid of a triangle is ⅔ of the distance any vertex of the triangle to the midpoint of the side opposite to it.

This implies that:

XN = ⅔(XG)

XG = 33

Substitute

XN = ⅔(33)

XN = 2*11

XN = 22

Please help!!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees in the forest that will be infected after t years.
f(t) = e^0.4t
1. The scientists believe the forest will be seriously damaged when 21 or more of the forest’s 200 oak trees are infected by oat wilt. According to their model, how many years will it take for 21 of the trees to become infected?

Type the correct answer in the box. Use numerals instead of words. Round your answer to the nearest tenth.

2. Rewrite the exponential model as a logarithmic model that calculates the number of years g (x) for the number of infected trees to reach a value of x.

Answers

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:

It will take 7.6 years for 21 of the trees to become infected.The logarithmic model is: [tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

Number of trees infected after t years:

The number of trees infected after t years is given by:

[tex]f(t) = e^{0.4t}[/tex]

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

[tex]f(t) = 21[/tex]

Thus:

[tex]e^{0.4t} = 21[/tex]

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

[tex]\ln{e^{0.4t}} = \ln{21}[/tex]

[tex]0.4t = \ln{21}[/tex]

[tex]t = \frac{\ln{21}}{0.4}[/tex]

[tex]t = 7.6[/tex]

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

[tex]f(x) = y = e^{0.4x}[/tex]

[tex]e^{0.4y} = x[/tex]

Again, we apply the natural logarithm to both sides of the equation, so:

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761

What is the length of side s of the square shown below? 450 90" A. 4-3 B. 1 C. 4 D. 2 E F. 2.5​

Answers

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

s² + s² = 2²

2s² = 4 ( divide both sides by 2 )

s² = 2 ( take the square root of both sides )

s = [tex]\sqrt{2}[/tex]

Answer:

E.

Step-by-step explanation:

we know the diagonal of the square : 2

as you can see in the picture, there is a right-angled triangle with the baseline of Hypotenuse being the diagonal, and 2 times s being the 2 sides.

that means we can use Pythagoras to calculate s :

2² = s² + s²

4 = 2s²

2 = s²

s = sqrt(2)

In ΔFKR, which side is included between ∠F and ∠R?

Answers

Answer:

First choice

Step-by-step explanation:

It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.

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