Question

Suppose $f\left(x\right)={(x+1)}^2$ for $x\ge -1$. If $g\left(x\right)$ is the function whose graph is the reflection of the graph of $f\left(x\right)$ with respect to the line $y=x$, then $g\left(x\right)$ is equal to

• A. $-\sqrt{x}-1$ for $x\ge 0$
• B. $\frac{1}{{(x+1)}^2}$ for $x>-1$
• C. $\sqrt{x+1}$ for $x>-1$
• D. $\sqrt{x}-1$ for $x\ge 0$

Answer 1

The correct option is D $\sqrt{x}-1$ for $x\ge 0$

$g\left(x\right)=f^{-1}\left(x\right)$
$y=(x+1{)}^2$
$\sqrt{y}=x+1$
$\sqrt{y}-1=x$
$g\left(x\right)=f^{-1}\left(x\right)=\sqrt{x}-1$ for $x\ge 0$