Question

If f(x) and f^-4(x) are inverse functions of each other and f(x) = 2x+5, what is f^-1(x)?

Answer 1

For this case we must find the inverse of the following function:

$f (x) = 2x + 5$

Then, we follow the steps:

We change $f (x)$by y:

$y = 2x + 5$

We exchange the variables:

$x = 2y + 5$

We clear the variable "y":

$x-5 = 2y\\y = \frac {x-5} {2}$

We change y for $f^{-1}(x):$

$f^{-1}(x) = \frac {x-5} {2}$

Answer:

$f^{-1}(x) = \frac {x-5} {2}$