Let `f: Nvec` be a function defined as `f(x)=9x^2+6x-5.` Show that `f: NvecS ,` where `S` is the range of `f,` is invertible. Find the inverse of `f` and hence `f^(-1)(43)` and `f^(-1)(163)dot`

Explanation

Given: `f: N arrow N` is a function defined as `quad f(x)=9 x^{2}+6 x-5`


Let `y=f(x)=9 x^{2}+6 x-5`



`Rightarrow {y}=9 x^{2}+6 {x}-5 `


`Rightarrow {y}=9 x^{2}+6 {x}+1-1-5 `


`Rightarrow {y}=(9 x^{2}+6 {x}+1)-6 `


`Rightarrow {y}=(3 x+1)^{2}-6 `


`Rightarrow {y}+6=(3 x+1)^{2}`


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