Question

Question 49.Graph each function and its inverse on the same set of axis. Label two points on graph?

Answer 1

`y=\log _8x`

To find the inverse of the logarithmic function, let's switch the places of x and y. It becomes:

`x=\log _8y`

After that, let's convert the logarithmic function to its equivalent exponential function.

`\begin{gathered} 8^x=y \\ 8^x=f^(-1)(x) \end{gathered}`

The inverse of the logarithmic function is 8^x.

Let's graph the two equations.

We labeled two points on each graph. As you can see, the points are at an equal distance from the line x = y, therefore, we got the correct inverse of the logarithmic function.