Functions
Functional Equations
JEE Main 2016
Grade 12
Question:
If $f(x) + 2f\left(\frac{1}{x}\right) = 3x$, $x \neq 0$, and $S = \{x \in \mathbb{R} : f(x) = f(-x)\}$, then $S$:
(1) is an empty set
(2) contains exactly one element
(3) contains exactly two elements
(4) contains more than two elements
Step-by-Step Solution
Key Concept: Substitute $x \to 1/x$ in the given equation to get a second equation. Solve the system for $f(x)$, then set $f(x) = f(-x)$ and solve.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)