Let `f: N -> R` be a function defined as `f(x)=4x^2+12 x+15.` Show that `f: N -> S,` where `S` is the range of `f` is invertible. Also find the inverse of `f`

Explanation

a function is invertible only one-one and onto

`x_1,x_2 in R`

`f(x_1)=f(x_2)`

`x_1=x_2`

`4x_1^2+12x_1+15=4x_2^2+12x_2+15`

`4(x_1^2-x_2^2)+12(x_1-x_2)=0`

`(x_1-x_2)(x_1+x_2)+3(x_1-x_2)=0`

`(x_1-x_2)[x_1+x_2+x_3]=0`

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