Question

If $f\left(x\right)=x+2;g\left(x\right)=x;h\left(x\right)=x^2$, then $ho\left(gof\right)\left(x\right)=$

• A. $x+2$
• B. $x^2$
• C. $x$
• D. $(x+2{)}^2$

Answer 1

The correct option is D $(x+2{)}^2$

$f\left(x\right)=x+2$;$q\left(x\right)=x,h\left(x\right)=x^2$

$qof\left(x\right)=q\left(f\right(x\left)\right)=f\left(x\right)$

$[\because q(1)=x]$

$\Rightarrow qof\left(1\right)=f\left(x\right)$

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

$\Rightarrow h\left(qof\right(1\left)\right)=\left[qof\right(x){]}^2$ $[\because h(1)=x^2]$

$=\left(f\right(x){)}^2$

$=(x+2{)}^2$