Question

For the following pair of functions, find (f+g)(x) and (f-g)(x).

f(x)= 4x2 + 7x-5 and g(x)= - 9x² + 4x - 13
(f+g)(x) = 0
(Simplify your answer. Type in descending order.)
(f-g)(x) =
(Simplify your answer. Type in descending order.)

Answer 1

Given:

The functions are

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

`g(x)=-9x^2+4x-13`

To find:

The functions
`(f+g)(x)` and
`(f-g)(x)`.

Solution:

We know that,

`(f+g)(x)=f(x)+g(x)`

`(f+g)(x)=4x^2+7x-5-9x^2+4x-13`

`(f+g)(x)=(4x^2-9x^2)+(7x+4x)+(-5-13)`

`(f+g)(x)=-5x^2+11x-18`

And,

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

`(f-g)(x)=(4x^2+7x-5)-(-9x^2+4x-13)`

`(f+g)(x)=4x^2+7x-5+9x^2-4x+13`

`(f+g)(x)=(4x^2+9x^2)+(7x-4x)+(-5+13)`

`(f-g)(x)=13x^2+3x+8`

Therefore, the required functions are
`(f+g)(x)=-5x^2+11x-18`

and
`(f-g)(x)=13x^2+3x+8`.