Question

1. Let f(x) = 7x2 – 5x + 3 and g(x) = 2x2 + 4x – 6.

Part A: Find f(x) + g(x)
Part B: Find f(x) – g(x)
Part C: Find g(x) – f(x)

Answer 1

f(x) + g(x) =
`9x^(2) - x - 3`

f(x) - g(x) =
`5x^(2) - 9x + 9`

g(x) - f(x) =
`-5x^(2) + 9x - 9`

Explanation:

`f(x) = 7x^(2) - 5x + 3\ and\ g(x) = 2x^(2) + 4x - 6`

Case 1:

f(x) + g(x)

=
`7x^(2) - 5x + 3 + (2x^(2) + 4x - 6)`

=
`7x^(2) - 5x + 3 + (2x^(2) + 4x - 6)`

=
`9x^(2) - x - 3`

Case 2:

f(x) - g(x)

=
`7x^(2) - 5x + 3 - (2x^(2) + 4x - 6)`

=
`7x^(2) - 5x + 3 - 2x^(2) - 4x + 6`

=
`5x^(2) - 9x + 9`

Case3:

g(x) - f(x)

=
`2x^(2) + 4x - 6 - (7x^(2) - 5x + 3)`

=
`2x^(2) + 4x - 6 - 7x^(2) + 5x - 3`

=
`-5x^(2) + 9x - 9`