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CAT 1991 — QA Question 11

Basics (Functions)Easy

A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same structure and form. Which of the following functions has this property?  

Answer & solution

Correct answer: y = 2 x + 3 3 x - 2

  • A

    y = 2x+33x+4

  • y = 2x+33x-2

  • C

    y = 3x+44x-5

  • D

    None of the above

Solution

For each of the given expressions, you may have to simplify and express x in terms of y and hence verify for which one does the form & structure remain the same.

In general, any function of the form y = ax+bbx-a reflects on to itself as we can rearrange it as

x = ay+bby-a

Let us check option (b).

y = f(x)

⇒ y = 2x+33x-2

⇒ 3xy - 2y = 2x + 3

⇒ 3xy - 2x = 2y + 3

⇒ x(3y - 2) = (2y + 3)

⇒ x = 2y+33y-2

∴ x = f(y)

Hence, the answer is (b).

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CAT 1991 QA Q11: A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same stru — Solution | TheCATExam