Question

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

Answer 1

`f(k^(-1))=-1` and `f^(-1)(2)=k^2`

Explanation:

As `f(x)=log_k (x)`

`f(k^(-1))=log_k (k^(-1))=(-1)log_k k=-1` and

For `f^(-1)(2)`, we will have to find inverse function of `f(x)`.

As `f(x)=log_k (x)`, `x=k^f(x)` and hence `f^(-1)(x)=k^x` and

`f^(-1)(2)=k^2`