CAT 2024 Slot 3 QA Question 15

Multiple choice (+3 / −1) · Algebra · Functions · Try it, then check the answer and solution below.

CAT 2024 Slot 3QAAlgebra • FunctionsModerate

For any non-zero real number x, let

f(x) + 2 f(\frac{1}{x}) = 3x

. Then, the sum of all possible values of

x

for which $f(x) = 3 , is

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⌨️ Shortcuts:[1-4 / A-D] Select[Enter] Check[B] Star[S] Solution

Official Convenor Answer Key: D

Answer and solution

Answer: D) -3

📌 Core Concept

The problem involves solving a functional equation and finding the sum of roots of a quadratic equation. The key steps involve setting up a system of equations to solve for the function

f(x)

and then using the quadratic formula or Vieta's formulas to find the sum of the roots.

🔢 Step-by-Step Solution

Given Functional Equation:

f(x) + 2 f\left(\frac{1}{x}\right) = 3x \quad \text{(1)}

Substitute

x

with

\frac{1}{x}

\[ f\left(

\frac{1}{x}

\right) + 2 f(x) =

\frac{3}{x}

\quad \text{(2)} \

CAT 2024 Slot 3 QA Question 15

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