Composite Function Value Calculation

CAT 2017 Slot 2 · QA · Medium · Functions

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Let f(x)=x2f(x) = x^2 and g(x)=2xg(x) = 2^x, for all real xx. Then the value of f(f(g(x))+g(f(x)))f( f(g(x)) + g(f(x)) ) at x=1x = 1 is

  1. A.

    16

  2. B.

    18

  3. C.

    36

  4. D.

    40

Answer

C

Explanation

At x=1x = 1: g(1)=21=2g(1) = 2^1 = 2 f(1)=12=1f(1) = 1^2 = 1

Now, evaluate f(g(1))f(g(1)): f(2)=22=4f(2) = 2^2 = 4

Evaluate g(f(1))g(f(1)): g(1)=21=2g(1) = 2^1 = 2

Sum =f(g(1))+g(f(1))=4+2=6= f(g(1)) + g(f(1)) = 4 + 2 = 6.

Finally, f(6)=62=36f(6) = 6^2 = 36.

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