Question

Suppose that the functions fand g are defined for all real numbers x as follows.f(x)=x+5g(x)=2x²Write the expressions for (g+f)(x) and (g–f)(x) and evaluate (g.f)(-3).

Answer 1

The expression (g+f)(x) is equal to g(x)+ f(x), (g-f)(x) is equal to g(x) f(x) and the expression (g*f)(-3) is equal to g(-3)*f(-3).

Then, we have

$(g+f)(x)=g(x)+f(x)=2x^2+x+5$

Similarly,

$(g-f)(x)=g(x)f(x)=2x^2-(x+5)=2x^2-x-5$

And finally,

$\begin{gathered} (g\cdot f)(-3)=g(-3)\cdot f(-3)=2(-3)^2\cdot(-3+5) \\ (g\cdot f)(-3)=2(9)\cdot(2) \\ (g\cdot f)(-3)=36 \end{gathered}$

In summary, the answers are:

$\begin{gathered} (g+f)(x)=2x^2+x+5 \\ (g-f)(x)=2x^2-x-5 \\ (g\cdot f)(-3)=36 \end{gathered}$