Question

For the exponential function f, find f^-1 analytically and graph both f and f^-1.f(x)=5^x-1

Answer 1

Given the function :

$f(x)=5^x-1$

We will find the inverse of the function analytically as following :

$y=5^x-1$

Solve for x

$\begin{gathered} y+1=5^x \\ x=\log _5(y+1) \end{gathered}$

make y in the place of x. so,

$\begin{gathered} y=\log _5(x+1) \\ \\ f^{-1}(x)=\log _5(x+1) \end{gathered}$

The graph of both function will be as shown in the following picture .

The given function f(x) = 5^x - 1 is the graph of the blue color

And the inverse with the red color

each function is written closer to its graph