Functions 1 Question 12
12. If $f(x)=\sin \log \frac{\sqrt{4-x^{2}}}{1-x}$, then the domain of $f(x)$ is… .
(1985, 2M) 13. The domain of the function $f(x)=\sin ^{-1} \log _2 \frac{x^{2}}{2}$ is given by …
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Answer:
Correct Answer: 12. $(-2,1)$
Solution:
- Given, $f(x)=\sin \log \frac{\sqrt{4-x^{2}}}{1-x}$
For domain, $\frac{\sqrt{4-x^{2}}}{1-x}>0,4-x^{2}>0$ and $1-x \neq 0$
$$ \begin{array}{lrll} \Rightarrow & (1-x)>0 & \text { and } & 4-x^{2}>0 \\ \Rightarrow & x<1 & \text { and } & |x|<2 \Rightarrow-2<x<1 \end{array} $$
Thus, domain $\in(-2,1)$.
