Suppose `f(x)=(x+1)^2` for`xgeq-1.` If `g(x)` is the function whose graph is the reflection of the graph of `f(x)` with respect to the line `y=x ,` then `g(x)` equal. (a)`1-sqrt(x-1),xgeq0` (b) `1/((x+1)^2),x gt-1` (c)`sqrt(x+1,)xgeq-1` (d) `sqrt(x)-1,xgeq0`

Options

A. `1-sqrt(x)-1, x ge 0`
B. `(1)/((x+1)^(2)),x gt -1 `
C. `sqrt(x+1), x ge -1`
D. `sqrt(x)-1, x ge 0`

Answer

D

Explanation

Given that `f(x)=(x+1)^(2), x ge -1.`
Now, if g(x) is the reflection of f(x) in the line y = x, then g(x) is an inverse function of `y = f(x).`
Given `y=(x+1)^(2) (x ge -1 and y ge 0)`
` or x = +- sqrt(y)-1`
` or g(x) =f^(-1)(x)=sqrt(x)-1, x ge 0`