If f (x) = 1/9 x-2, what is f-1(x)?

Answers

Answer 1

Given:

The function is:

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

To find:

The value of [tex]f^{-1}(x)[/tex].

Solution:

We have,

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=\dfrac{1}{9}x-2[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{1}{9}y-2[/tex]

Step 3: Isolate the variable [tex]y[/tex].

[tex]x+2=\dfrac{1}{9}y[/tex]

[tex]9(x+2)=y[/tex]

[tex]9x+18=y[/tex]

[tex]y=9x+18[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=9x+18[/tex]

Therefore, the required function is [tex]f^{-1}(x)=9x+18[/tex].


Related Questions

A regular hexagon has a perimeter of 150 m. Find its area. Leave your answer in the simplest radical form.

Answers

Answer:

1623.80 m²

√3(1875/2) m²

Step-by-step explanation:

The area, A of a regular hexagon can be obtained using the relation :

A = √3(p²/24)

The perimeter, p = 150 m

Therefore,

A = √3(150²/24)

A = √3(22500/24)

A = √3(937.5)

A = 1623.7976

A = 1623.80 m²

A = √3(1875/2) m²

Solve the equation for x.

Answers

Answer:

x = 7

Step-by-step explanation:

2x + 34 = 4x + 20

2x = 14

x = 7

can someone please help me i need to calculate the are of a trapezium which is 6cm 15cm 9cm, please help

Answers

Answer:

Step-by-step explanation: The parallel sides of a trapezium are called the bases and the distance between them is the height. Therefore if 6cm and 15cm are the bases and 9cm is the height, then the area is A= ½(b1+b2)×h, where b1 is 6cm and b2 is 15cm and h is 9cm. Therefore the Area= ½(6+15)×9=94,5cm.

Answer:

shush its hard like my

Step-by-step explanation:

put 0.6 as a percent

Answers

Answer:

6%

Step-by-step explanation:

Select the correct answer.

If function f has zeros at -3 and 4, which graph could represent function f?

A.
the graph of a quadratic function y = (1/4)(x+3)(x-4)
B.
the graph of a quadratic function y = -(1/4)(x-3)(x+4)
C.
the graph of a quadratic function y = -(x+3)(x+4)
D.
the graph of a quadratic function y = (x-3)(x-4)

Answers

A is valid
It is the only option where y(-3) and y(4) are both zero

Which is true regarding chords and diameters of circles?

Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.
Both chords and diameters have two endpoints on a circle. Chords must intersect the center of a circle.
Chords have two endpoints on a circle. Diameters have one endpoint on a circle and one at the center.
Chords have one endpoint on a circle and one at the center. Diameters have two endpoints on a circle.

Answers

The state that is valid is

"Every diameter of a circle is also a chord because a chord of a circle is any line segment joining two points on the circumference of the circle."

What is a diameter

A diameter is a line that divides a circle into two halves, a diameter is also a chord

What is a Chord

A chord is a line that connects points on a circle, a chord is not a diameter because it does not divide a circle into two equal halves

Learn more about circles here:

https://brainly.com/question/10458894

What are the solution(s) to the quadratic equation 50 – X2 = 0?
[tex]2 \sqrt{5} [/tex]
[tex] 6\sqrt{3} [/tex]
no real solution​

Answers

Answer:

Step-by-step explanation:

50 - x² = 0

50 = x²

x² = 50

x = √50

[tex]x = \sqrt{2*5*5}\\\\x=5\sqrt{2}[/tex]

Answer:

[tex]50 - {x}^{2} = 0 \\ {x}^{2} = 50 \\ x = \sqrt{50} \\ x = 5 \sqrt{2} [/tex]

An equilateral triangle with side length 20 cm is shown in the diagram, work out the area of the triangle.Give your answer rounded to 1 DP.

Answers

Answer:

173.2 cm²

Step-by-step explanation:

Use the equilateral triangle area formula, A = [tex]\frac{\sqrt{3}}{4}[/tex]

Plug in the side length and solve:

A = [tex]\frac{\sqrt{3}}{4}[/tex]a²

A = [tex]\frac{\sqrt{3}}{4}[/tex](20)²

A = [tex]\frac{\sqrt{3}}{4}[/tex](400)

A = 173.2

So, the area of the triangle is approximately 173.2 cm²

help pls. cant figure it out

Answers

Answer:

m=3

Step-by-step explanation:

add the m on the right side, 4m+3=15

subract the 3 on the left side, 4m=12

divide by four to isolate m, m=3

Answer:

[tex]3m+3=15-m[/tex]

[tex]3m+3=-m+15[/tex]

[tex]3m+m=15-3[/tex]

[tex]4m=12[/tex]

[tex]Divide\ both\ sides \ by\ 4[/tex]

[tex]\frac{4m}{4} =\frac{12}{4}[/tex]

[tex]\boxed{\boxed{\underline{\textsf{\textbf{m=3}}}}}[/tex]

-------------------------hope it helps...have a great day!!

can someone assist me with this, has me mad
drop menu 1:
A. y-axis
B. x-axis
C. line y=x
D. line y=-x
drop menu 2:
A. 4 units to the right and 10 units up
B. 8 units to the right and 4 units up
C. 10 units to the right and 2 units up
D. 10 units to the right and 4 units up​

Answers

Answer:

A. y-axis

B. x-axis

C. line y=x

D. line y=-x

drop menu 2:

A. 4 units to the right and 10 units up

B. 8 units to the right and 4 units up

C. 10 units to the right and 2 units up

D. 10 units to the right and 4 units up​

Answer:

C, and D

Step-by-step explanation:

First you reflect over the line y=x (line goes diagonal from quadrant I to quadrant III)

The rule of reflecting over the y=x line is that point (x,y) becomes point (y,x)

For example, point C ( -4, 2), becomes C' ( 2, -4)

Second is a translation 10 units to the right and 4 units up from C'(2,-4) to C''(0, 12)

5 - 3tan3x = 0 trên -π< x < π.

Answers

Answer:

x = 0.343

Step-by-step explanation:

We want to solve:

5 - 3tan(3x) = 0

such that:

-π< x < π

where π = 3.14

then:

-3.14 < x < 3.14

Let's solve the equation:

5 - 3tan(3x) = 0

-3tan(3x) = -5

tan(3x) = -5/-3 = 5/3

Now we can use the inverse tan function, Atan(x).

Remember that:

Atan( tan(x) ) = tan( Atan(x)) = x

Then if we apply that function to both sides, we get:

Atan( tan(3x)) = Atan(5/3)

3x = Atan(5/3)

x = Atan(5/3)/3 = 0.343

Describe how you would factor x^2 + 10x - 24. Be specific.

Answers

Answer:

if u have more doubts feel free to ask :)

Step-by-step explanation:

x² + 10x -24  

x² + 12x - 2x - 24          

x(x + 12) -2(x + 12)

(x + 12) (x - 2)

Factors of 24 : ±1 , ±2 , ±3 , ±4 , ±6 , ±8 , ±12,  ±24. Combination of +12 and -2 gives "10" the middle term also " 24"

A ball was kicked off a picnic table at the park and its height, h, in metres, above the ground after time, t, in seconds, is represented by h = 0.5 + 16t- 2t^2.

a) What is the height of the picnic table?

b) Complete the square to determine the maximum height of the ball? ​

Answers

Step-by-step explanation:

the picnic table height is 0.5 because it's the constant

and the maximum height is 28

my answer is in the image above

How do I solve and what's the answer?

Answers

Answer:

Step-by-step explanation:

A parallelogram is a family of quadrilateral which has its two opposite sides to be equal and parallel.

In the given parallelogram, the following proof can be deduced.

1. QS bisects RT: <RSQ ≅ <TQS                    Given

2. RV ≅ TV                                                      Definition of a bisector

3. <SRQ + < RQT = [tex]180^{o}[/tex]                                  Definition of supplementary angles

4. <RQS ≅ <QST                                             Definition of alternate angles

5. <RVT ≅ <QVT                                             Vertically opposite angles

6. <QRS ≅ <STQ                                             Opposite angles are congruent

7. QRST is a parallelogram                             Proofed

Which point would not be a solution to the system of linear inequalities shown below? y\ge x+5\hspace{50px}y\ge\frac{2}{3} x+6 y≥x+5y≥ 3 2 ​ x+6 (12, 7) (-12, 1) (-12, 9) (-12, 6)

Answers

Answer:

(12,7) is not a solution

Step-by-step explanation:

Given

[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]

Required

Point that is not a solution

We have:

[tex]y\ge x+5\hspace{50px}y\ge\frac{2}{3}x + 6[/tex]

Substitute [tex]\frac{2}{3}x + 6[/tex] for y in the first inequality

[tex]\frac{2}{3}x + 6 \ge x + 5[/tex]

Collect like terms

[tex]\frac{2}{3}x - x \ge 5-6[/tex]

[tex]-\frac{1}{3}x \ge -1[/tex]

Solve for x (the inequality will change because we are to divide by a  negative number_

[tex]x \le -1/-\frac{1}{3}[/tex]

[tex]x \le 3[/tex]

Without solving further, we can conclude that the first option is not a solution.

Because (12,7) implies that [tex]x =12[/tex]

Compare [tex]x =12[/tex] to [tex]x \le 3[/tex], then [tex]x \le 3[/tex] is false

What is 1/root 2
Give me that ans asap

Answers

Answer:

1/√2

Approximate numerical value

1/√2 = 0.707106781186548

---------------------------

Rationalize the denominator

(1/√2) * (√2 / √2) = √2 / 2

pls help its my last day of school and a have only a few mins to submit

Answers

Answer:

slope = 1/2

y intercept = 2

slope intercept form = y = 1/2x + 2

Step-by-step explanation:

Answer:

Slope: 2

y-intercept: 2

Slope intercept form: y=2x+2

Step-by-step explanation:

Hope this helps!

6. A metal is made from copper, zinc and lead in the ratio 13:6:1
respectively. The mass of zinc is 90kg. Calculate the mass of the
metal. ​

Answers

Given:

A metal is made from copper, zinc and lead in the ratio 13:6:1.

The mass of zinc is 90kg.

To find:

The mass of the metal.

Solution:

It is given that the metal is made from copper, zinc and lead in the ratio 13:6:1.

Let the mass of copper, zinc and lead are 13x, 6x and 1x respectively.

The mass of zinc is 90kg. So,

[tex]6x=90[/tex]

[tex]x=\dfrac{90}{6}[/tex]

[tex]x=15[/tex]

Now, total mass of the metal is:

[tex]Total=13x+6x+1x[/tex]

[tex]Total=20x[/tex]

[tex]Total=20(15)[/tex]

[tex]Total=300[/tex]

Therefore, the mass of the metal is 300kg.

What is the measure of <JHM

25
45
50
90​

Answers

45 of course because it measured higher then others and it’s the systems of odd numbers

pleaseee helppp meeee!!!!

Answers

5x - 10 = 25 so first you have to add ten to both sides
5x-10=25
+10 +10
5x = 35
Then you divide both sides by 5
/5 /5
X = 7
And that’s how you get it!!

Please help asap!! I will mark you as brainliest :)

Answers

Answer:

3, 0, -5, -6

Step-by-step explanation:

7)

when x= -8, f(x) = 8-5 or 3

when x= -5 f(x) = 5-5 or 0

when x= 0, f(x) = 0-5 or -5

when x=1, f(x) = -1-5 or -6

Please help if you answer and some extra points!

Answers

Answer: if you go to symbolab it will definitely help you and yes i know i did not help whatsoever but just try it if not im sorry

Step-by-step explanation:

Answer the questions.

Answers

Answer:

5.

Objective C

[tex]125x + 200 \geqslant 1200 \\ 125x \geqslant 1000 \\ x \geqslant 8[/tex]

7

[tex]x \: \alpha \: y \\ y = kx \\ 2.00 = k \times 8 \\ k = \frac{2.00}{8} \\ k = 0.25[/tex]

What is the 30th term of the linear sequence below?
-4,-1,2,5,8...

Answers

Answer:

80

Step-by-step explanation:

-4,-1,2,5,8,11,14,17,20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,65,68,71,74,77,80.

Can someone help me with this?

Answers

Answer:

(b)

Step-by-step explanation:

7th grade math help me pleaseeee

Answers

Answer:

Step-by-step explanation:

the first one is a negative correlation

check the above for first

The 5th grade teacher ordered 32 pizzas for an end-of-year celebration for their students.

-Each pizza was cut into equal sized slices.
-Each slice was 1/8 of a pizza.
How many slices of pizza were there in all?

Answers

Answer:

256

Step-by-step explanation:

There were 32 pizzas cut into 8 slices, so multiply the number of slices per pizza by the number of pizzas.

Can anyone solve this question for me urgent! With work please. Thank you!

Answers

Answer:

P = 75*

Step-by-step explanation:

figure B is a scaled copy of figure A. What is the scale factor from figure A to B​

Answers

The scale factor from Figure A to Figure B is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is the scale factor
Let
z-----> the scale factor
In this problem

substitute values

the scale factor is less than 1
therefore
is a reduction

x- (-3) is the same as x + (-3).
O True
O False

Answers

Answer:

false

Step-by-step explanation:

because x - (-3)

= x+3

and x + - 3

= x - 3

so they are not the same

hope this helps

Answer:

False

Step-by-step explanation:

If u minus you go the opposite direction

And you have negative 3

So you do the opposite direction of -3 which is +3

So x+3

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