To find the inverse of the function [tex]\( f(x) = \frac{1}{2}x + 7 \)[/tex], follow these steps:
1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = \frac{1}{2}x + 7 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = \frac{1}{2}y + 7 \][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[ x - 7 = \frac{1}{2}y \][/tex]
4. Multiply both sides by 2 to isolate [tex]\( y \)[/tex]:
[tex]\[ 2(x - 7) = y \][/tex]
5. Simplify:
[tex]\[ y = 2x - 14 \][/tex]
Therefore, the inverse function is:
[tex]\[ f^{-1}(x) = 2x - 14 \][/tex]
So the correct answer is:
[tex]\[ \boxed{C. \ f^{-1}(x) = 2x - 14} \][/tex]
