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Consider f: R^+->[-5,\ oo) given by f(x)...

Consider `f: R^+->[-5,\ oo)` given by `f(x)=9x^2+6x+5` . Show that `f` is invertible with `f^(-1)(x)=(sqrt(x+6)-1)/3` .

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`f: R->[-5,oo)` given by `f(x)=9x^2+6x-5`.
Let `y` be an arbitrary element of `[-5,\ oo)`.
Let `y=9x^2+6x-5`
`implies y=(3x+1)^2-1-5`
`implies y=(3x+1)^2-6`
`implies (3x+1)^2 = y + 6`
`implies 3x+1=sqrt(y+6)`
`implies x=frac{sqrt(y+6)-1}{3}`
...
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