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Question: If \(f(x) = \frac{2x + 1}{3x - 2},\) then \((fof)(2)\) is equal to...

If f(x)=2x+13x−2,f(x) = \frac{2x + 1}{3x - 2}, then (fof)(2)(fof)(2) is equal to

A

1

B

3

C

4

D

2

Answer

2

Explanation

Solution

Here f(2)=54f(2) = \frac{5}{4}

Hence (fof)(2)=f(f(2))=f(54)=2×54+13×54−2=2(fof)(2) = f(f(2)) = f\left( \frac{5}{4} \right) = \frac{2 \times \frac{5}{4} + 1}{3 \times \frac{5}{4} - 2} = 2