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Suppose f(x)=(x+1)^2forxgeq-1. If g(x) i...

Suppose `f(x)=(x+1)^2forxgeq-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)/((x+1)^(2))xgt-1`

B

`-sqrt(x)-1`

C

`sqrt(x)+1`

D

`sqrt(x)-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=(x+1)^(2),x ge-1` and g(x) is reflection of graph f(x) in the line y = x, then g(x) is the inverse of f(x).
Let `y=(x+1)^(2)`, then
`sqrt(y)-1=x`
`:." "sqrt(x)-1=f^(-1)(x)`
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