To find the inverse of the function [tex]\( f(x) = \frac{x}{5} - 2 \)[/tex], we follow these steps:
1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = \frac{x}{5} - 2
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x = \frac{y}{5} - 2
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
- First, add 2 to both sides to isolate the fraction:
[tex]\[
x + 2 = \frac{y}{5}
\][/tex]
- Next, multiply both sides by 5 to solve for [tex]\( y \)[/tex]:
[tex]\[
5(x + 2) = y
\][/tex]
Therefore, the inverse function is:
[tex]\[
f^{-1}(x) = 5(x + 2)
\][/tex]
So, the correct option is:
D. [tex]\( f^{-1}(x) = 5(x + 2) \)[/tex]
