Answer:
2
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.