Question

if
`f(x)=(1)/(3) - (1)/(2)x` and
`g(x) = 2x^(2) + x + 4` find
`(f+g)(x)`

Answer 1

`\large\boxed{(f+g)(x)=2x^2+(1)/(2)x+4(1)/(3)}`

Explanation:

`(f+g)(x)=f(x)+g(x)\\\\\text{We have}\\\\f(x)=(1)/(3)-(1)/(2)x,\ g(x)=2x^2+x+4.\\\\\text{Substitute:}\\\\(f+g)(x)=\left((1)/(3)-(1)/(2)x\right)+(2x^2+x+4)\\\\=(1)/(3)-(1)/(2)x+2x^2+x+4\qquad\text{combine like terms}\\\\=2x^2+\left(-(1)/(2)x+x\right)+\left((1)/(3)+4\right)\\\\=2x^2+(1)/(2)x+4(1)/(3)`