To find the inverse of the function [tex]\( f(x) = \frac{x}{5} + 3 \)[/tex], we need to follow these steps:
1. Start by replacing [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = \frac{x}{5} + 3
\][/tex]
2. Next, solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex].
Subtract 3 from both sides:
[tex]\[
y - 3 = \frac{x}{5}
\][/tex]
3. Multiply both sides by 5 to isolate [tex]\( x \)[/tex]:
[tex]\[
5(y - 3) = x
\][/tex]
4. Finally, replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex], as we are expressing the inverse function:
[tex]\[
f^{-1}(x) = 5(x - 3)
\][/tex]
Thus, the inverse function is:
[tex]\[
f^{-1}(x) = 5(x - 3)
\][/tex]
Comparing with the given options, we find that answer C matches.
So, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
