Question

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

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

Answer 1

The correct option is B $x^2+2$

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

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

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

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

Replacing $g\left(x\right)$ by $x$, we get-

$f\left(x\right)=2+x^2=x^2+2$

Answer-(B)