Question

Please help me find the inverse of f(x) = 2^x. I think that will help me label these?

Answer 1

Given function:

`f(x)=2^x`

To obtain the inverse of the function f(x), we follow the steps outlined below:

Step 1: Replace f(x) with y:

`y=2^x`

Step 2: Interchange x and y

`x=2^y`

Step 3: Solve for y:

`\begin{gathered} \text{Take logarithm of both sides} \\ \log x=log2^y \\ y\log 2\text{ = log x} \\ \text{Divide both sides by log2} \\ y\text{ = }\frac{\log x}{\log \text{ 2}} \\ y\text{ = }\log _2x \end{gathered}`

Step 4: Replace y with f-1(x):

`f^(-1)(x)\text{ = }\log _2x`

Answer:

`f^(-1)(x)\text{ = }\log _2x`