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Symmetry of Functions

CAT 1993 Slot 1 · Quantitative Ability · Easy · QA

This is an easy Quantitative Ability question from the CAT 1993 Slot 1 paper. It tests QA. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A function f(x)f(x) is said to be even if f(−x)=f(x)f(-x)=f(x), and odd if f(−x)=−f(x)f(-x) = -f(x). The function given by f(x)=∣x∣3f(x) = |x|^3 is

  1. A.

    even

  2. B.

    odd

  3. C.

    neither

  4. D.

    both

Answer

A

Explanation

f(−x)=∣−x∣3=∣x∣3=f(x)f(-x) = |-x|^3 = |x|^3 = f(x). Thus f(x)f(x) is an even function.

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