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

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`

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`

Text Solution

AI Generated Solution

To find the function \( g(x) \), which is the reflection of the function \( f(x) = (x + 1)^2 \) with respect to the line \( y = x \), we can follow these steps: ### Step 1: Set up the equation for \( f(x) \) We have the function defined as: \[ f(x) = (x + 1)^2 \quad \text{for } x \geq -1. \] ...
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