Question

which function is the inverse of $f(x) = b^x$?

a. $f^{-1}(y) = \log_b y$

b. $f^{-1}(y) = \log_y b$

c. $f^{-1}(y) = \log_x b$

d. $f^{-1}(y) = \log_x y$

Explanation:

Step1: Let \( y = F(x)=b^x \)

To find the inverse, we need to solve for \( x \) in terms of \( y \).

Step2: Convert exponential to logarithmic form

Recall that if \( y = b^x \), then by the definition of logarithms, \( x=\log_b y \). So the inverse function \( F^{-1}(y)=\log_b y \).

Answer:

A. \( F^{-1}(y)=\log_{b}y \)