If f(0, ∞) → R is given by

Question:

If $f(0, \infty) \rightarrow R$ is given by $f(x)=\log _{10} x$, then $f^{-1}(x)=$

Solution:

Given: f(x) = log10x

$f(x)=\log _{10} x$

$\Rightarrow y=\log _{10} x$

$\Rightarrow x=10^{y}$

Thus, $f^{-1}(y)=10^{y}$.

Hence, $f^{-1}(x)=10^{x}$.

 

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