Question

Q1 : Find the inverse of the function.

Answer 1

Answer:

1. Option D is correct.

2. Option B is correct.

3. Option B is correct.

Step-by-step explanation:

Inverse function defined as the the function that undergoes the action of the other function.

A function $f^{-1}$ is the inverse of f if whenever y =f(x) and $x =f^{-1}$

To find the inverse of the function:

Q1.

Given the function:  f(x) = 7x -1

Put y for f(x) and solve for x;

y= 7x -1

Add 1 both sides we get;

y + 1 = 7x

Divide both sides by 7 we get;

$x = \frac{y+1}{7}$

Put $f^{-1}(y)$ for x;

$f^{-1}(y) = \frac{y+1}{7}$

Interchange y =x, we have

$f^{-1}(x) = \frac{x+1}{7}$

Q 2.

Given the function:

$f(x) = x^3 - 7$

Put y for f(x) and solve for x;

$y = x^3-7$

Add 7 both sides we get;

$y + 7 =x^3$

taking cube root both sides we get

$x =\sqrt[3]{y+7}$

Put $f^{-1}(y)$ for x;

$f^{-1}(y) =\sqrt[3]{y+7}$

Interchange y =x, we have

$f^{-1}(x) = \sqrt[3]{x+7}$

Q3 .

Given the function:

$f(x) = 5x^3 - 3$

Put y for f(x) and solve for x;

$y = 5x^3-3$

Add 3 both sides we get;

$y + 3 =5x^3$

Divide both sides by 5 we get;

$x^3 = \frac{y+3}{5}$

taking cube root both sides we get

$x = \sqrt[3]{\frac{y+3}{5} }$

Put $f^{-1}(y)$ for x;

$f^{-1}(y) = \sqrt[3]{\frac{y+3}{5} }$

Interchange y =x, we have

$f^{-1}(x) = \sqrt[3]{\frac{x+3}{5} }$