Question

Select the correct answer.

Find the inverse of function f.
f (x) = 9x + 7
A. f^{\small -1}(x)\ =\ 7x\ +\ 9
B. f^{\small -1}(x)\ =\ -9x\ -\ 7
C. f^{\small -1}(x)\ =\ \frac{1}{9}x\ -\ \frac{7}{9}
D. f^{\small -1}(x)\ =\ \frac{7}{9}x\ -\ \frac{1}{9}

Answer 1

`(x-7)/(9)`

which corresponds to choice
C :
`f^(\small -1)(x)\ =\ (1)/(9)x\ -\ (7)/(9)`

Explanation:

The inverse of a function y = f(x) can be found by interchanging x and y and solving for y

Let y = f(x)

y = 9x + 7

Interchange x and y:

x = 9y + 7

9y + 7 = x (switch sides)

subtract 7 both sides
→ 9y + 7 - 7 = x - 9

→ 9y = x - 9

Divide both sides by 9

→
`y = (x - 7)/(9) = (x)/(9) - (7)/(9)`

which corresponds to choice C