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

User PeerBr
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1 Answer

4 votes

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.

User Matt Mower
by
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