Question

If $f\left(x\right)=\{\begin{array}{c}x+1,ifx\le 1\\ 5-x^{2}ifx>1\end{array},g\left(x\right)=\{\begin{array}{c}xifx\le 1\\ 2-xifx>1\end{array}$

and $x\in (1,2)$, then $g\left(f\right(x\left)\right)$ is equal to

• A. $x^2+3$
• B. $x^2-3$
• C. $5-x^2$
• D. $1-x$

Answer 1

Answer: (B)

$x^2-3$

$xϵ(1,2)$

Hence for x >1, $f\left(x\right)=5-x^2$and $f\left(x\right)ϵ(1,4)$

$f\left(x\right)>1$

$g\left(f\right(x\left)\right)=2-f\left(x\right)=2-5+x^2=x^2-3$