Question

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

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

Answer 1

The correct option is B $\sqrt{x}-1$

$g\left(x\right)$ will be the inverse function of $f\left(x\right)$

Now let $y=f\left(x\right)=(x+1{)}^2$

$\Rightarrow \sqrt{y}=x+1$, as $x\ge -1$

$\Rightarrow x=\sqrt{y}-1=f^{-1}\left(y\right)$

$\therefore g\left(x\right)=f^{-1}\left(x\right)=\sqrt{x}-1$