To find the inverse of the function [tex]\( f(x) = 2x - 10 \)[/tex], we follow these steps:
1. Rewrite the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 2x - 10 \][/tex]
2. Interchange [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[ x = 2y - 10 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
- Add 10 to both sides of the equation:
[tex]\[ x + 10 = 2y \][/tex]
- Divide both sides by 2:
[tex]\[ y = \frac{x + 10}{2} \][/tex]
4. Simplify the expression:
[tex]\[ y = \frac{x}{2} + 5 \][/tex]
Thus, the inverse function is:
[tex]\[ f^{-1}(x) = \frac{x}{2} + 5 \][/tex]
So, among the given options, the correct inverse function is:
[tex]\[ h(x) = \frac{1}{2} x + 5 \][/tex]
The correct answer is:
[tex]\[ \boxed{h(x)=\frac{1}{2} x+5} \][/tex]
