Question

If $f\left(x\right)=(x-1{)}^2$ and $g\left(x\right)=\sqrt{x}$, then $\left(g_{\circ }f\right)\left(x\right)=$

• A. $|x-1|$
• B. $x-1$
• C. $1-x$
• D. $\sqrt{x}(x-1{)}^2$
• E. $(\sqrt{x}-1{)}^2$

Answer 1

The correct option is A $|x-1|$

Given, $f\left(x\right)={(x-1)}^2$ and $g\left(x\right)=\sqrt{x}$
$\therefore \left(gof\right)\left(x\right)=g\left(f\right(x\left)\right)$

$=g\left({(x-1)}^2\right)$

$=\sqrt{{(x-1)}^2}$

$=|x-1|$