Question

Suppose that the functions and g are defined for all real numbers x as follows. f(x) = x + 3; g(x) = 2x - 2 Write the expressions for (fg)(x) and (f - g)(x) and evaluate (f + g)(3)

Answer 1

Given

`\begin{gathered} f(x)=x+3 \\ \\ g(x)=2x-2 \end{gathered}`

Then

`(f\cdot g)(x)=f(x)\cdot g(x)=(x+3)(2x-2)=2x^2+4x-6`

`(f-g)(x)=f(x)-g(x)=(x+3)-(2x-2)=x-2x+3+2=5-x`
`(f+g)(3)=f(3)+g(3)=(3+3)+(2(3)-2)=6+4=10`