The inverse of this function would be f(x) = [tex] \frac{Log(x - 1)}{Log3} [/tex].
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) = [tex] 3^{x} [/tex] - 1 ----> Switch f(x) and x
x = [tex] 3^{f(x)} [/tex] - 1 ----> Add 1 to both sides
x + 1 = [tex] 3^{f(x)} [/tex] -----> 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
[tex] \frac{Log(x - 1)}{Log3} [/tex] = f(x) ----> And switch the order for formatting purposes.
f(x) = [tex] \frac{Log(x - 1)}{Log3} [/tex]
And that would be your new inverse function.
