Question

F(x)=x/2-2 and g(x)=2x^2+x-3 find (f+g)(x)

Answer 1

`\large\boxed{(f+g)(x)=2x^2+(3)/(2)x-5}`

Explanation:

`(f+g)(x)=f(x)+g(x)\\\\f(x)=(x)/(2)-2=(1)/(2)x-2\\\\g(x)=2x^2+x-3\\\\(f+g)(x)=\left((1)/(2)x-2\right)+(2x^2+x-3)\\\\=(1)/(2)x-2+2x^2+x-3\qquad\text{combine like terms}\\\\=2x^2+\left((1)/(2)x+x\right)+(-2-3)\\\\=2x^2+1(1)/(2)x-5\\\\=2x^2+(3)/(2)x-5`