Let f:[0,infinity) - R be a function given by f(x) = 9x^2 + 6x - 5, show that f is - Maths - Relations and Functions

Question

Let f:[0,infinity) ->R be a function given by f(x) = 9x^2 + 6x -
5, show that f is not invertible Modify the codomain of f to make f
invertible and then find the inverse of f

Rahul Raj · Accepted Answer

dear student

let y=f(x)=9x2+6x-5=9x2+6x+1-6=(3x+1)2-6(3x+1)=y+6x=y+6-13for x to be defined y+6≥0y≥-6but given co=domain=R hence function is not invertibleit will be invertible when function isf:[0,∞)->[-6,∞)y=f(x)=9x2+6x-5f-1(x)=x+6-13

regards

Let f:[0,infinity) ->R be a function given by f(x) = 9x^2 + 6x - 5, show that f is not invertible. Modify the codomain of f to make f invertible and then find the inverse of f.