Question #N137
The function f is defined by $f(x) = \frac{1}{2}x - 3$. What is the value of $f^{-1}(5)$?
A. -4
B. -1
C. 4
D. 14
Correct Answer is: D
To find the inverse function, $f^{-1}(x)$, we first swap $x$ and $y$ in the equation $y = f(x)$: $x = \frac{1}{2}y - 3$. Solving for $y$, we get $2x + 6 = y$. Thus, $f^{-1}(x) = 2x + 6$. Substituting 5 for $x$ in this equation gives $f^{-1}(5) = 2(5) + 6$, or $f^{-1}(5) = 16$.