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CAT 1999 — QA Question 37

Composite FunctionsEasy
Passage / Data

Directions: Answer the questions based on the following information.
Let x and y be real numbers and let
f (x,y) = |x + y| , F(f (x,y)) = −f (x,y)
and G(f (x, y)) = −F(f (x, y))

Which of the following expressions yields x2 as its result?

Answer & solution

  • A

    F(f (x, − x))⋅G(f (x, − x))

  • B

    F(f (x, x))⋅G(f (x, x))⋅ 4

  • -F(f(x, x)) ∙ G(f(x, x)) ÷ log2 16

  • D

    f (x, x)⋅ f (x, x)

Solution

f (x,y) = |x + y| − − − This is always positive
F(f (x,y)) = − f (x,y) = −|x + y| − − − This is always negative
G(f (x,y)) = − F(f (x,y)) = − (−|x + y|) = |x + y| − − − This is always positive.

The option (c) yields x2.

-F(f(x, x)) ∙ G(f(x, x)) ÷ log2 16

= -(-2x ∙ 2x) ÷ log2 16

= 4x2log224=x2

CAT 1999 QA Q37: Which of the following expressions yields x 2 as its result? — Solution | TheCATExam