Question

The function $f:(0,\infty )\to (-\infty ,\infty )$ is defined by $f\left(x\right)={\log }_{3}x$ then $f^{-1}\left(x\right)=$

• A. $3^x$
• B. $3^{-x}$
• C. $-3^x$
• D. $-3x^{-x}$

Answer 1

Answer: (A)

$3^x$

$f\left(x\right)={\log }_{3}x$
$f^{-1}:(-\infty ,\infty )\to (0,\infty )$
Let ${\log }_{3}x=y=f\left(x\right)$
$\Rightarrow x=3^y$
$f\left(x\right)=y\Rightarrow f^{-1}\left(y\right)=x=3^y$
$\therefore f^{-1}\left(x\right)=3^x$