The functions $f ( x ) = 3 ^ { x }$ and $g ( x )$ are inverse functions. Find the $g ( x )$
A) $g ( x ) = \log _ { 3 } x$
B) $g ( x ) = \ln x$
C) $g ( x ) = \sqrt [ 3 ] { x }$
D) $g ( x ) = x ^ { 3 }$
E) $g ( x ) = \log x$

Question

Quizplus · Accepted Answer

If $f(x) = 3^x$ and $g(x)$ are inverse functions then $f(g(x))=x$ and $g(f(x))=x$. Substituting $f(x)=3^x$, we get $g(3^x) = x$. Solving for $g(x)$, we get $g(x) = \log_3(x)$. Therefore, the answer is A.

The Functions f(x)=3xf ( x ) = 3 ^ { x }f(x)=3x

The Functions $f ( x ) = 3 ^ { x }$