Question

If $f\left(x\right)=\sqrt{x+3}$ and $g\left(x\right)=x^2+1$, then $f\left(g\right(x)$ =

• A. $\sqrt{x^2+4}$
• B. $x+4$
• C. $x+4$
• D. $\sqrt{x^2+3}$

Answer 1

The correct option is A $\sqrt{x^2+4}$

$f\left(x\right)=\sqrt{x+3}$
$g\left(x\right)=x^2+1$

$f\left(g\right(x)=\sqrt{g\left(x\right)+3}$
$=\sqrt{x^2+1+3}$
$=\sqrt{x^2+4}$