Question

If f ( x )=3 x2+4 x−2∧g ( x)=x2−2x+3 , Find an expression for ( f - g)(x)

Answer 1

`(f-g)(x) = 2x^2+ 6x-5`

Explanation:

Given

`f(x) = 3x^2 + 4x - 2`

`g(x) = x^2 - 2x + 3`

Required

Find
`(f-g)(x)`

In functions:

`(f-g)(x) = f(x) - g(x)`

Substitute values for f(x) and g(x)

`(f-g)(x) = 3x^2 + 4x - 2 - (x^2 - 2x + 3)`

Open bracket

`(f-g)(x) = 3x^2 + 4x - 2 - x^2 + 2x - 3`

Collect Like Terms

`(f-g)(x) = 3x^2 - x^2+ 4x + 2x- 2 - 3`

`(f-g)(x) = 2x^2+ 6x-5`