Question

If $f\left(x\right)=(1-x)$ , $x\in \left[-3,3\right]$ , then the domain of $f\left(f\left(x\right)\right)$ is

• A. $\left[-2,3\right]$
• B. $\left(-2,3\right)$
• C. $[-2,3]$
• D. $(-2,3]$

Answer 1

The correct option is C $[-2,3]$

$f\left(x\right)=1-x$

$f\left(f\left(x\right)\right)=f(1-x)=1-1+x=x$

And $x\in [-3,3]$

Domain of $f\left(x\right)$ is $[-3,3]$

Domain of $f\left(f\left(x\right)\right)=$Domain of $f(1-x)$

Domain of $f\left(f\left(x\right)\right)=[1-3,3]=[-2,3]$