Question

Let f: `[0,oo) rarr R` be a function defined by `f(x) = 9 x^2 + 6x - 5`. Prove that f is not invertible Modify, only the codomain of f to make f invertible and then find its inverse.

Answer 1

`f(x)=9x^2+6x-5`
`D=36-4*9*(-5)=216`
`(-b/20,-D/40)=(-1/3,-216/36)=(-1/3,-6)`
`x>=0`
`f(x)>=-5`
Range`in`[-5,`oo`)
`R in `Co-domain
`y=9x^2+6x-5`
`y=(3x+1)^2-6`
`(3x+1)^2=y+6`
`(3x+1)=sqrt(y+6)`
`x=(sqrt(y+6)-1)/3`
`f^(-1)(x)=(sqrt(x+6)-1)/3`.