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CAT 1991 — QA Question 24

Basics (Functions)Easy

If y = f(x) and f(x) = (1–x)(1+x), which of the following is true?

Answer & solution

Correct answer: x = f(y)

  • A

    f(2x) = f(x) - 1

  • B

    x = f(2y) - 1

  • C

    f(1/x) = f(x)

  • x = f(y)

Solution

y = f(x) = 1-x1+x

⇒ y(1 + x) = 1 – x

⇒ y + xy = 1 – x

⇒ x + xy = 1 – y

⇒ x(1 + y) = (1 – y)

⇒ x = 1-y1+y = f(y)

Since here, y = f(x) and x = f(y), the given function refleccts on itself.

Hence, option (d).

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CAT 1991 QA Q24: If y = f(x) and f(x) = ( 1 – x ) ( 1 + x ) , which of the following is true? — Solution | TheCATExam