Question

How to find the inverse function of h(x)= 2^x ?

Answer 1

`h(x) = log_2(x)`

Explanation:

The find the inverse of an invertible function `y = f(x)`, swap `y` and `x` and solve for `y`.

We have `h(x) = y = 2^x`. Swapping `x` and `y` gives `x = 2^y`. We now wish to solve for `y`.

Take the log with base 2 of both sides of the equation to free the `y` variable.

`x = 2^y`
`log_2 (x) = log_2(2^y) = y`

Thus, `y = h(x) = log_2 (x)`. See that we used the fact that `log_n(n^x) = x`.