Question

Write the inverse of h(x) = e 2x
h -1(x) =

log e2 x
2log ex
½log ex

Answer 1

C

Explanation:

We are given the function.

`h(x)=e^(2x)`

And we want to find its inverse.

Let's switch h(x) and x and change h(x) to h⁻¹(x). Hence solve:

`\displaystyle \begin{aligned} x & = e^{2h^(-1)(x)} \\ \\ \ln x & = \ln e^{2h^(-1)(x)} \\ \\ \ln x & = 2h^(-1)(x) \\ \\ h^(-1)(x) & = (1)/(2) \ln x\end{aligned}`

In conclusion, our answer is C.

Note:

`\ln(x)=\log_ex`