Question

select the correct answer. find the inverse of function f. f(x) = 9x + 7 a. f⁻¹(x) = (7/9)x - 1/9 b. f⁻¹(x) = 7x + 9 c. f⁻¹(x) = (1/9)x - 7/9 d. f⁻¹(x) = -9x - 7

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start with the function \( f(x) = 9x + 7 \). Replace \( f(x) \) with \( y \), so we have \( y = 9x + 7 \).

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x = 9y + 7 \).

Step3: Solve for \( y \)

First, subtract 7 from both sides of the equation: \( x - 7 = 9y \).
Then, divide both sides by 9: \( y=\frac{x - 7}{9}=\frac{1}{9}x-\frac{7}{9}\).

Step4: Replace \( y \) with \( f^{-1}(x) \)

We replace \( y \) with \( f^{-1}(x) \) to get the inverse function. So, \( f^{-1}(x)=\frac{1}{9}x - \frac{7}{9}\).

Answer:

C. \( f^{-1}(x)=\frac{1}{9}x - \frac{7}{9} \)