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Let \( f:(-1, \infty) \rightarrow R \) be defined by \( f(0)=1 \) and \( f(x)= \)\( \frac{1}{x} \log _{e}(1+x), x \neq 0…

Q1

Let \( f:(-1, \infty) \rightarrow R \) be defined by \( f(0)=1 \) and \( f(x)= \)\( \frac{1}{x} \log _{e}(1+x), x \neq 0 \). Then the function \( f \) :

[JEE Main 2020, 2 Sep (Shift 2)]

a

increases in \( (-1, \infty) \)

b

increases in \( (-1,0) \) and decreases in \( (0, \infty) \)

c

decreases in \( (-1,0) \) and increases in \( (0, \infty) \)

d

decreases in \( (-1, \infty) \)

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