Question

If f(x)=x/2-3 and g(x)=4x^2+x-4, find (f+g)(x)

Answer 1

`\large\boxed{(f+g)(x)=4x^2+(3)/(2)x-7}`

Explanation:

`(f+g)(x)=f(x)+g(x)\\\\f(x)=(x)/(2)-3=(1)/(2)x-3,\ g(x)=4x^2+x-4\\\\\text{Substitute:}\\\\(f+g)(x)=\left((1)/(2)x-3\right)+(4x^2+x-4)\\\\=(1)/(2)x-3+4x^2+x-4\qquad\text{combine like terms}\\\\=4x^2+\left((1)/(2)x+x\right)+(-3-4)\\\\=4x^2+1(1)/(2)x-7\\\\=4x^2+(3)/(2)x-7`