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Composite Function Value

CAT 2017 Slot 1 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If f(x)=5x+23x−5f(x) = \frac{5x + 2}{3x - 5} and g(x)=x2−2x−1g(x) = x^2 - 2x - 1, then the value of g(f(f(3)))g(f(f(3))) is:

  1. A.

    2

  2. B.

    13\frac{1}{3}

  3. C.

    6

  4. D.

    23\frac{2}{3}

Answer

A

Explanation

f(3)=5(3)+23(3)−5=174f(3) = \frac{5(3) + 2}{3(3) - 5} = \frac{17}{4}. f(f(3))=f(174)=5(17/4)+23(17/4)−5=85/4+251/4−5=93/431/4=3f(f(3)) = f\left(\frac{17}{4}\right) = \frac{5(17/4) + 2}{3(17/4) - 5} = \frac{85/4 + 2}{51/4 - 5} = \frac{93/4}{31/4} = 3. So f(f(3))=3f(f(3)) = 3. g(f(f(3)))=g(3)=32−2(3)−1=9−6−1=2g(f(f(3))) = g(3) = 3^2 - 2(3) - 1 = 9 - 6 - 1 = 2.

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