Let's find the values step-by-step.
### Part (a): Find [tex]\( f(2) \)[/tex]
Given the function [tex]\( f(x) = \frac{x+5}{x} \)[/tex], we need to find [tex]\( f(2) \)[/tex].
1. Substitute [tex]\( x = 2 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(2) = \frac{2 + 5}{2}
\][/tex]
2. Perform the arithmetic:
[tex]\[
f(2) = \frac{7}{2} = 3.5
\][/tex]
So, [tex]\( f(2) = 3.5 \)[/tex].
### Part (b): Find [tex]\( f^{-1}(2) \)[/tex]
Given the inverse function [tex]\( f^{-1}(x) = \frac{5}{x-1} \)[/tex], we need to find [tex]\( f^{-1}(2) \)[/tex].
1. Substitute [tex]\( x = 2 \)[/tex] into the inverse function [tex]\( f^{-1}(x) \)[/tex]:
[tex]\[
f^{-1}(2) = \frac{5}{2 - 1}
\][/tex]
2. Perform the arithmetic:
[tex]\[
f^{-1}(2) = \frac{5}{1} = 5.0
\][/tex]
So, [tex]\( f^{-1}(2) = 5.0 \)[/tex].
### Summary
The results are:
- [tex]\( f(2) = 3.5 \)[/tex]
- [tex]\( f^{-1}(2) = 5.0 \)[/tex]
