Question

How do you find `f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)` given `f(x)=x^2-2x` and `g(x)=x+9`?

Answer 1

`f(x) + g(x) = x^2-x +9`
`f(x) - g(x) = x^2-3x-9`
`f(x) * g(x) = x^3+7x^2-18x`
`(f/g)(x) = (x(x-2))/(x+9)`

Explanation:

Substitute the functions into the equations and add like-terms:

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

Distribute the negative and add like-terms:
`f(x) - g(x) = x^2-2x - (x+9) = x^2-2x -x-9`
`= x^2-3x-9`

Distribute and add like-terms:
`f(x) * g(x) = (x^2-2x)(x+9) = x^3+9x^2-2x^2-18x`
`= x^3+7x^2-18x`

Factor numerator:
`(f/g)(x) = (x^2-2x)/(x+9) = (x(x-2))/(x+9)`