Question

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

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

Answer 1

The correct option is B

$\sqrt{x^2+4}$

We know that $fog\left(x\right)=f\left(g\right(x\left)\right).$

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

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