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CAT 2017 Slot 2 — QA Question 23

Composite FunctionsEasy

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

Answer & solution

  • A

    16

  • B

    18

  • 36

  • D

    40

Solution

We have to calculate f [f(g(x)) + g(f(x))]

First we need to calculate f(g(x)) and g(f(x))

At x = 1, f[g(x)] = f[g(1)]
Now g(1) = 21 = 2
f[g(1)] = f(2) = 4

At x = 1, g[f(x)] = g[f(1)]
Now f(1) = 1 and
g[f(1)] = g(1) = 21 = 2

Now at x = 1
f [f(g(x)) + g(f(x))] = f(4 + 2) = f(6) = 36

Hence, option (c).

CAT 2017 Slot 2 QA Q23: Let f(x) = x 2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is — Solution | TheCATExam