Question

If f(x)=x/3-2and g(x)=3x^+2x-6 find (f+g) (x)

Answer 1

Given

$\begin{gathered} f(x)=\frac{x}{3}-2 \\ g(x)=3x^2+2x-6 \end{gathered}$

We want to find (f + g)(x). This is basically the sum function of f and g.

We add the two functions and simplify. The steps are shown below:

$\begin{gathered} (f+g)(x)=f(x)+g(x) \\ =(\frac{x}{3}-2)+(3x^2+2x-6) \\ =\frac{x}{3}-2+3x^2+2x-6 \\ =3x^2+2x+\frac{x}{3}-2-6 \\ =3x^2+\frac{7}{3}x-8 \end{gathered}$

The correct answer is:

$(f+g)(x)=3x^2+\frac{7}{3}x-8$