Question

Write the inverse of f(x) = 3^x - 1

Answer 1

The inverse of this function would be f(x) = $\frac{Log(x - 1)}{Log3}$.

You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.

f(x) = $3^{x}$ - 1 ----> Switch f(x) and x

x = $3^{f(x)}$ - 1 ----> Add 1 to both sides

x + 1 = $3^{f(x)}$ -----> Take the logarithm of both sides in order to get the f(x) out of the exponent

Log(x + 1) = f(x)Log3 ----> Now divide both sides by Log3

$\frac{Log(x - 1)}{Log3}$ = f(x) ----> And switch the order for formatting purposes.

f(x) = $\frac{Log(x - 1)}{Log3}$

And that would be your new inverse function.