Question

Given f(x) = x² + 4x -5find f(x) inverse

Answer 1

The function is given as

`f(x)=x^2+4x-5`

To find the inverse of the function ,

`y=x^2+4x-5`

Replace x with y.

`x=y^2+4y-5`

Now solve for y,

Add 4 and subtract 4 in the RHS.

`x=y^2+4y-5+4-4`
`x=y^2+4y-9+4`
`x=(y+2)^2-9`
`x+9=(y+2)^2`
`(y+2)^2=x+9`
`y+2=\pm\sqrt[]{x+9}`
`y=\sqrt[]{x+9}-2`
`y=-\sqrt[]{x+9}-2`

Hence the inverse of the function is

`y=\sqrt[]{x+9}-2,-\sqrt[]{x+9}-2`