The domain and range for the function f(x)=e^ d x x are - Vidyadip

MCQ

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

✓
domain $=R$, range $(0, \infty)$
B
domain $=R$, range $=R$
C
domain $=R$, range $=[0, \infty)$
D
domain $=R$, range $=[1, \infty$ )

✓

Answer

Correct option: A.

domain $=R$, range $(0, \infty)$

(a) : $f(x)=e^{|x| \sin x}$
We know that domain of $|x|$ is from $(-\infty, \infty)$ and domain of $\sin x$ is also from $(-\infty, \infty)$
So, domain of $f(x)=e^{|x| \sin x}$ is from $(-\infty, \infty)$
We know that range of expononential function is from $(0, \infty)$. So, range of function $f(x)=e^{x \mid \sin x}$ is from $(0, \infty)$.

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