Question

If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f (x) = 2x + 5, what is

Answer 1

Answer:

See explanation

Step-by-step explanation:

The question has conflicting details

$f(x) = 2x + 5$

$f(x) = 2x + 5$ and three halves doesn't sound correct.

So, I will take f(x) as

$f(x) = 2x + 5$

Next, solve for the inverse function

Replace f(x) with y

$y = 2x + 5$

Swap x and y

$x = 2y + 5$

Make 2y the subject

$2y = x-5$

Make y the subject

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

Replace y with the inverse sign

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

So, now we can calculate any value from the original function and from the inverse function.

For instance:

$f^{-1}(7) = \frac{7-5}{2} = \frac{2}{2} = 1$

$f(1) = 2*1 + 5 = 2+5=7$