Mathematics College

What is the inverse of function f?

Answers

Answer 1

9514 1404 393

Answer:

D. f^-1(x) = 3 -7x

Step-by-step explanation:

Solve x = f(y) for y to find the inverse function.

x = f(y)

x = (3 -y)/7 . . . . . . use the function definition

7x = 3 -y . . . . . . . .multiply by 7

y = 3 -7x . . . . . . . add y-7x to both sides

Then the inverse function is ...

[tex]\boxed{f^{-1}(x)=3-7x}[/tex]

Related Questions

How to find Joint and Combined variation?

Answers

Answer:

W is multiplied by 8

Step-by-step explanation:

If W varies jointly with x, y, and z, we can say that

W = k (xyz), with k being a constant for our original equation. We are asked what will happen to W if x, y, and z are each doubled. To figure this out, we can go back to our equation,

W = k (xyz)

First, we can double x, meaning that we multiply it by 2. Doing this, we get

W = k (2x * y * z)

Then, we can double y and z in a similar fashion, resulting in

W = k (2x * 2y * 2z)

W = 8 * k (xyz)

The new W, after all the doubling, is equal to 8 * k * x * y * z. The old W is equal to k * x * y * z. It can be determined that the new W is equal to 8 * the old W, so W is multiplied by 8

solve 3 1/5 = y - 12/25

Answers

3 1/5 = y - 12/25

31/5+y = -12/25

31+y = -12/25×5

31+y = -12/5

y = -12/5-31

y = -143/5

y = -28.6

HOPE IT HELPS

Need the answer please, soon as possible

Answers

9514 1404 393

Answer:

(d) 27.4%

Step-by-step explanation:

The desired percentage is ...

(juniors for Kato)/(total juniors) × 100%

= 129/(129 +194 +147) × 100%

= (129/470) × 100% ≈ 27.4%

About 27.4% of juniors voted for Kato.

Find an equation of the circle whose diameter has endpoints (-6, -1) and (-2,3).

Answers

Step-by-step explanation:

Let find the distance of the diameter. using distance formula.

[tex](3 + 1) {}^{2} + ( - 2 + 6) {}^{2} = \sqrt{8} [/tex]

The diameter is sqr root of 8 units.

A circle equation is

[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]

where r is the radius. The radius is half the diameter so

[tex]r = \frac{ \sqrt{8} }{2} = \frac{ \sqrt{8} }{ \sqrt{4} } = \sqrt{2} [/tex]

[tex] {r}^{2} = { \sqrt{2} }^{2} = 2[/tex]

So our radius is 2.

Now we need to find the midpoint or Center of the diameter.

[tex] \frac{ - 6 - 2}{2} = - 4[/tex]

[tex] \frac{3 - 1}{2} = 1[/tex]

So the center of the circle is (-4,1). So our equation of the Circle us

[tex](x + 4) {}^{2} + (y - 1) {}^{2} = ( \sqrt{2} ) {}^{2} [/tex]

For each of the indicates values given for x and y, determine which expression has a greater value (x+y)^2 or (x-y)^2

Answers

We can’t see the indicate values, but for a general answer, the first will be better AS LONG AS Y IS A POSITIVE. The second answer will be better if Y is a negative. Hope this helps.

find the slope of the line that passes through these two points

Answers

Answer:

Step-by-step explanation:

When A = 200, solve the equation x2 - 40x + A=0 using the quadratic formula. Show all your working and give your answers correct to 2 decimal places.

Answers

Answer:

Solution given:

equation is:

x²-40x+A=0

when A=200

equation becomes

x²-40x+200=0

Comparing above equation with ax²+bx+c=0 we get

a=1

b=-40

c=200

By using quadratic equation formula

x=[tex]\displaystyle \frac{-b±\sqrt{b²-4ac}}{2a}[/tex]

substituting value

x=[tex]\displaystyle \frac{-*-40±\sqrt{(-40)²-4*1*200}}{2*1}[/tex]

x=[tex]\displaystyle \frac{40±\sqrt{800}}{2}[/tex]

x=[tex]\displaystyle \frac{40±20\sqrt{2}}{2}[/tex]

taking positive

x=[tex]\displaystyle \frac{40+20\sqrt{2}}{2}[/tex]

x=34.14

taking negative

x=[tex]\displaystyle \frac{40-20\sqrt{2}}{2}[/tex]

x=5.86

x=34.14 or 5.86

Which decimal is equivalent to
15/100?
A- O 0.015
B- 0.15
C-o 1.5
D- 0.0015

Answers

Answer:

Step-by-step explanation:

0.0015

hope this helps

B - 0.15

hope this will help you !
good luck

Casey's phone service charges a flat monthly fee of $30 for the first 1000 minutes of calls and $0.40 per minute over 1000. Determine Casey's monthly charge if he makes 1,100 minutes of calls?

Answers

Answer:

Casey's monthly charge for making 1,100 minutes of calls is $70.

Step-by-step explanation:

We can write a piecewise function to model the situation.

Since Casey's phone service only charges a monthly fee of $30 for the first 1000 minutes, we can write that for calling t minutes:

[tex]\displaystyle C(t) = 30\text{ if } t\leq 1000[/tex]

In other words, the total cost is only $30 is the total minutes of call is less than 1000 minutes.

However, if the total minutes of calls is greater than 1000, then its $0.40 per minute on top of the 30. Thus:

[tex]\displaystyle C(t) = 30 + 0.4(t-1000)\text{ if } t>1000[/tex]

All together, our piecewise function will be:

[tex]\displaystyle C(t) = \begin{cases} 30 & t\leq 1000 \\ 30 + 0.4(t-1000) & t>1000\end{cases}[/tex]

We want to determine Caseys monthly charge if he makes 1,100 minutes of calls. So, t = 1100. Since 1100 > 1000, we will use the second equation. This yields:

[tex]C(1100)= 30+0.4((1100)-1000)[/tex]

Evaluate:

[tex]\displaystyle C(1100) = 30+0.4(100) = 30+40=\$70[/tex]

Casey's monthly charge for using 1,100 minutes of call is $70.

Write the polynomial in standard form. Then name the polynomial based on its degree and number of
terms.
y-7y3 + 15y9

Answers

Answer:

[tex]15y^9 - 7y^3 + y[/tex]

Nonic polynomial

Step-by-step explanation:

Given

[tex]y - 7y^3 + 15y^9[/tex]

Required

Write in standard form

The standard form of a polynomial is:

[tex]ay^n + by^{n-1} + ......... + k[/tex]

So, we have:

[tex]y - 7y^3 + 15y^9[/tex]

The standard form is:

[tex]15y^9 - 7y^3 + y[/tex]

And the name is: Nonic polynomial (because it has a degree of 9)

find the area of the circle use 3.14 for pi d=4 m

Answers

Answer:

The area of circle is 12.56m sq.

PLEASE HELP

Solve the equation for y. Identify the slope and y-intercept then graph the equation.

-3y=3x-9

Y=
M=
B=

Please Include a picture of the graph and show your work if you can

Answers

9514 1404 393

Answer:

y = -x +3

m = -1

b = 3

Step-by-step explanation:

To solve the given equation for y, divide by the coefficient of y.

(-3y)/(-3) = (3x -9)/(-3)

y = -x +3

The slope is the x-coefficient, M = -1.

The y-intercept is the added constant, B = 3.

Both equations are graphed in the attachment. Texture has been added to the original so you can see the graphs are the same line.

For the given annual rate of change, find the corresponding growth or decay factor. + 300%

Answers

Answer:

50% growth would would be (1 + .5)^ n

and 100% growth would be (1+ 1)^n

I assume that the answer would be (1+3)^n

for 300% growth the factor would be 3

Step-by-step explanation:

A window has the shape of a semicircle. The base of the window is measured as having diameter 64 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum error possible in computing the area of the window.
a. 1.3π cm^2
b. 2.4 πcm^2
c. 2.6 πcm^2
d. 3.2 πcm^2
e. 1.6 πcm^2
f. 1.2 πcm^2

Answers

Answer:

e. 1.6π cm²

Step-by-step explanation:

Since the window is in a semi-circular shape, its area A = πD²/4 ÷ 2 = πD²/8 where D = diameter of window = 64 cm

Now, the error in the area dA = dA/dD × dD where dD = error in the diameter = 0.1 cm and dA/dD = derivative of A with respect to D.

So, dA/dD = d(πD²/8)/dD = 2 × πD/8 = πD/4

So, the differential dA = dA/dD × dD

dA = πD/4 × dD

Substituting D = 64 cm and dD = 0.1 cm into the equation, we have

dA = πD/4 × dD

dA = π × 64 cm/4 × 0.1 cm

dA = π × 16 cm × 0.1 cm

dA = π × 1.6 cm²

dA = 1.6π cm²

So, the maximum error in computing the area of the window is 1.6π cm²

find the exact value of tan(165°) using a difference of two angles

Answers

Answer: [tex]-2+\sqrt{3}[/tex]

=========================================================

Work Shown:

Apply the following trig identity

[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]

Now let's rationalize the denominator

[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]

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

As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.

Or you can note how

[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]

which helps us see that they are the same thing.

Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.

The firm had 15 billion VND of earnings before interest and tax (EBIT), corporate tax is 20%. The market price of stock is 60.000đ. Knowing that net income will be held 40% before using it for dividend. How much of the net income can be divided for shareholders?