Question

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

log3 x - 1
log3 x + 1
log3 (x - 1)

Answer 1

Answer:

$f^{-1}(x)=log_3(x+1)$

Step-by-step explanation:

Function f(x) is defined as: $f(x)=3^x-1$

In order to find its inverse ($f^{-1} (x)$, we need in the first step, to replace f(x) by the variable "y": $f(x)=3^x-1\\y=3^x-1$

In the next step, we solve for "x" as a function of "y". Notice that we need to use the logarithm base 3 to bring the exponent "x" down:

$y=3^x-1\\y+1=3^x\\log_3(y+1)=log_3(3^x)=x\\x=log_3(y+1)$

Next, we replace y with "x", and x with $f^{-1}(x)$

$x=log_3(y+1)\\f^{-1}(x)=log_3(x+1)$