Given f (x) = 2x5 + 12, what is the value of (f-1 o f) (2) ?

2

Step-by-step explanation:

You are trying to find (f' o f) (2). This means that you need to put f (x) into f' (x) and solve for 2.

First, find f' (x). To do this, take the original function and switch the x and y values.

y = 2x⁵ + 12

x = 2y⁵ + 12

x - 12 = 2y⁵

(x - 12) / (2) = y⁵

y = ⁵√ (x - 12) / (2)

Now, you need to put f (x) into the inverse function through the x-value. Simplify completely.

y = ⁵√ ((2x⁵ + 12) - 12) / (2)

y = ⁵√ ((2x⁵) / (2)

y = ⁵√x⁵

y = x

Now plug in the value given to you.

(f⁻¹ o f) (2) = 2

The answer is 2.