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  • If <img alt="f\left ( x \right )=log\left ( 1-x \right ),g\left ( x \right )=x^{2}" src="/latex-image/?f%5Cleft%20%28%20x%20%5Cright%20%29%3Dlog%5Cleft%20%28%201-x%20%5Cright%20%29%2Cg%5Cleft%20%28

If f\left ( x \right )=log\left ( 1-x \right ),g\left ( x \right )=x^{2} , then the domain of fog\left ( x \right ) is

Option: 1

\left ( -\infty,-1 \right )\cup \left ( 1,\infty \right )

 

 


Option: 2

(-1,1]


Option: 3

\left ( -1,1 \right )


Option: 4

None of these


Answers (1)

best_answer

f o g(x)=f(g(x))=\log \left(1-x^{2}\right)

For its domain, we find values of x  for which \log \left(1-x^{2}\right)  is defined
\begin{aligned} &\Rightarrow \quad\left(1-x^{2}\right)>0 \\ &\Rightarrow \quad x^{2}-1<0 \\ &\Rightarrow \quad(x+1)(x-1)<0 \\ \end{aligned}

 

\begin{aligned} &\Rightarrow \quad x \in(-1,1) \end{aligned}

Posted by

HARSH KANKARIA

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