If f ( x ) = e x − 1 x + 2 x + 1 then f ( x ) is

f ( x ) = e x − 1 x + 2 x + 1 f ( − x ) = e − x − 1 − x − 2 x + 1 = e x − 1 x e x − 2 x + 1 = e x − 1 x + 2 x + 1

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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsEven-oddMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

A function $f (x)$ is said to be even if $f (- x) = f (x)$ and odd if $f (- x) = - f (x)$ . Also, $f (x)$ is said to be periodic if $f (x + T) = f (x)$ for $T > 0$ , and the least positive value $T$ is called its period.

If $f (x) = \frac{x}{e ^{x} - 1} + \frac{x}{2} + 1$ then $f (x)$ is

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Solution:

$f (x) = \frac{x}{e ^{x} - 1} + \frac{x}{2} + 1$ $f (- x) = \frac{- x}{e ^{- x} - 1} - \frac{x}{2} + 1 = \frac{x e ^{x}}{e ^{x} - 1} - \frac{x}{2} + 1 = \frac{x}{e ^{x} - 1} + \frac{x}{2} + 1$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Even-odd

⏱ 2mℹ️ Source: QB

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