Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Reflection of a function about the line y=x is nothing but finding the inverse of the function. So the question basically is to find the inverse of f(x)

$y=(x+1{)}^2$
$\sqrt{y}-1=x$
Replace y with x gives inverse function of f(x)
$f^{-1}\left(x\right)=\sqrt{x}-1$