Let $f(x) = \log_3{\sqrt{x}}$, for $x 0$. Show that $f^{-1}(x) = 3^{2x}$.

Question

Let $f(x) = \log_3{\sqrt{x}}$, for $x > 0$. Show that $f^{-1}(x) = 3^{2x}$. Write down the range of $f^{-1}$. Let $g(x) = \log_3{x}$, for $x >0$. Find the value of $(f^{-1} \circ g)(2)$, giving your answer as an integer.

Accepted Answer

(a) $f^{-1}(x)=3^{2x}$ (b) $(0,\infty)$ (c) $4$

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions

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