Question

Suppose f(×) = 2^×, sketch a graph of f(×) and f^-1(×)​

Answer 1

Let f(x) = y

y = 2^x

x = 2^y

Solve for y.

ln x = ln(2^y)

ln x = y ln 2

ln x/ln 2 = y

Replace y with f^(-1) x.

f^(-1) x = ln x/ln 2

We now know f(x) and f^(-1) x.

Use your graphing calculator to graph the function and its inverse on the same xy-plane. If you don't have a graphing calculator, use DESMOS online.

Good luck.