Answer :
Given the function:
f(x) = 9x + 7
Let's find the inverse of the function.
To find the inverse of the function interchange variables and solve for y.
Take the following steps:
• Step 1.
Rewrite f(x) as y.
y = 9x + 7
• Step 2.
Interchange the variables:
x = 9y + 7
• Step 3.
Let's solve for y.
Subtract 7 from both sides
x - 7 = 9y + 7 - 7
x - 7 = 9y
• Step 4.
Divide all terms by 9:
[tex]\begin{gathered} \frac{x}{9}-\frac{7}{9}=\frac{9y}{9} \\ \\ \frac{x}{9}-\frac{7}{9}=y \\ \\ y=\frac{x}{9}-\frac{7}{9} \end{gathered}[/tex]Therefore, the inverse of the given function is:
[tex]f^{-1}(x)=\frac{1}{9}x-\frac{7}{9}[/tex]ANSWER: D
[tex]f^{-1}(x)=\frac{1}{9}x-\frac{7}{9}[/tex]