# If f(x)=log_k(x), find f(k^(-1)) and f^(-1)(2)?

Oct 27, 2016

$f \left({k}^{- 1}\right) = - 1$ and ${f}^{- 1} \left(2\right) = {k}^{2}$

#### Explanation:

As $f \left(x\right) = {\log}_{k} \left(x\right)$

$f \left({k}^{- 1}\right) = {\log}_{k} \left({k}^{- 1}\right) = \left(- 1\right) {\log}_{k} k = - 1$ and

For ${f}^{- 1} \left(2\right)$, we will have to find inverse function of $f \left(x\right)$.

As $f \left(x\right) = {\log}_{k} \left(x\right)$, $x = {k}^{f} \left(x\right)$ and hence ${f}^{- 1} \left(x\right) = {k}^{x}$ and

${f}^{- 1} \left(2\right) = {k}^{2}$