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Let f:[-1,oo]vec[-1,) is given by f(x)=(...

Let `f:[-1,oo]vec[-1,)` is given by `f(x)=(x+1)^2-1,xgeq-1.` Show that `f` is invertible. Also, find the set `S={x :f(x)=f^(-1)(x)}dot`

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Injectivity : Let `x` and `y in[-1,infty)`, such that

`f(x)=f(y) `

`Rightarrow(x+1) 2-1=(y+1) 2-1 `

`Rightarrow(x+1) 2=(y+1) 2 `

`Rightarrow(x+1)=(y+1) `

`Rightarrow x=y`

...
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