Question

Which is the inverse of the function f(x) = x - 9?АО1f-1(x) =x + 9B.f-'(x) = x + 9CO $-+(x) = 9 - *D.F-'-) =-X-9

Answer 1

To solve for the inverse of the function given;

$f(x)=x-9$

We begin by re-writing the function as follows;

$y=x-9$

To now find the inverse, we interchange y for x, and vice versa, as shown below;

$\begin{gathered} y=x-9 \\ \text{Now becomes;} \\ x=y-9 \end{gathered}$

We now find the value of y;

$\begin{gathered} x=y-9 \\ \text{Add 9 to both sides;} \\ x+9=y-9+9 \\ x+9=y \\ y=x+9 \\ \text{Therefore;} \\ f^{-1}(x)=x+9 \end{gathered}$

ANSWER:

The correct answer is option B;

$f^{-1}(x)=x+9$