JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q61

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MathematicsSingle correct+4 / -1Question 61 of 90

If $f(x)+2f\left(\dfrac1x\right)=3x$ , $x\ne0$ , and $S=\{x\in\mathbb R:f(x)=f(-x)\}$ ; then S :

is an empty set.

contains exactly one element.

contains exactly two elements.

contains more than two elements.

Answer and worked solution

Official answer: C

Replacing $x$ by $\frac1x$ : $f\left(\frac1x\right)+2f(x)=\frac3x$ . Solving the pair, $f(x)=\frac2x-x$ . Then $f(x)=f(-x)$ gives $\frac4x=2x$ , so $x=\pm\sqrt2$ : exactly two elements.

Topics:Types of functions Sets and operations

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 61