The domain and range for the function $f(x)=e^{|x| \sin x}$ are domain $=$ IR

The domain and range for the function $f(x)=e^{|x| \sin x}$ are domain $=$ IR
  1. range $=[0, \infty)$ domain $=$ IR
  2. range $=[1, \infty)$ domain $=$ IR
  3. range $=$ IR domain $=I R$
  4. range $=(0, \infty)$

Solution

$f(x)=e^{|x| \sin x}$ is defined every where Hence domain of $f(x)$ is $R$ $\begin{aligned} & \therefore-\infty < |x| \sin x < \infty . \\ & \Rightarrow 0 < e^{|x| \sin x} < \infty \\ & \Rightarrow \text { Range of } f(x) \text { is }(0, \infty) \end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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