Question

I need help with this

Answer 1

`\begin{gathered} f(x)=x^2+3 \\ g(x)=-2x+6 \\ a)(f+g)(3)= \\ (f+g)(x)=x^2+3-2x+6 \\ (f+g)(x)=x^2-2x+9 \\ \text{now, }(f+g)(3)\text{ means that x=3, hence} \\ (f+g)(3)=3^2-2(3)+9 \\ (f+g)(3)=9-6+9 \\ (f+g)(3)=12 \end{gathered}`
`\begin{gathered} b)\text{ (f-g)(-5)} \\ (f-g)(x)=x^2+3-(-2x+6) \\ (f-g)(x)=x^2+3+2x-6 \\ (f-g)(x)=x^2+2x-3 \\ \text{Now, }(f-g)(-5)\text{ means that x=-5, hence} \\ \text{ }(f-g)(-5)=(-5)^2+2(-5)-3 \\ \text{ }(f-g)(-5)=25-10-3 \\ \text{ }(f-g)(-5)=25-13 \\ \text{ }(f-g)(-5)=12 \end{gathered}`