Question

Assertion :Let $f\left(x\right)=\frac{1-x}{1+x}(x\ne -1)$ then $\left(fof\right)\left(\cos x\right)$ is equal to $\cos x$ Reason: $\left(fof\right)\left(x\right)$ is an identify function

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given $f\left(x\right)=\frac{1-x}{x+1}$

$\therefore \left(fof\right)\left(x\right)=f\left(f\left(x\right)\right)$

$\Rightarrow f\left(\frac{1-x}{1+x}\right)=\frac{1-\left(\frac{1-x}{1+x}\right)}{1+\left(\frac{1-x}{1+x}\right)}$

$\Rightarrow \left(fof\right)\left(x\right)=x$

$\therefore \left(fof\right)\left(\cos x\right)=\cos x$