Question

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

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

Answer 1

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

It is only to find the inverse.
Let $y=f\left(x\right)=(x+1{)}^2,forx\ge -1\Rightarrow \pm \sqrt{y}=x+1,x\ge -1\Rightarrow \sqrt{y}=x+1\Rightarrow y\ge 0,x+1\ge 0\Rightarrow x=\sqrt{y}-1\Rightarrow f^{-1}(y)=\sqrt{y}-1\Rightarrow f^{-1}(x)=\sqrt{x}-1\Rightarrow x\ge 0$