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}`