Question

if (x)=\frac{1}{3} - \frac{1}{2}x " alt="f(x)=\frac{1}{3} - \frac{1}{2}x " align="absmiddle" class="latex-formula"> and $g(x) = 2x^{2} + x + 4$ find $(f+g)(x)$

Answer 1

Answer:

$\large\boxed{(f+g)(x)=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}}$

Step-by-step explanation:

$(f+g)(x)=f(x)+g(x)\\\\\text{We have}\\\\f(x)=\dfrac{1}{3}-\dfrac{1}{2}x,\ g(x)=2x^2+x+4.\\\\\text{Substitute:}\\\\(f+g)(x)=\left(\dfrac{1}{3}-\dfrac{1}{2}x\right)+(2x^2+x+4)\\\\=\dfrac{1}{3}-\dfrac{1}{2}x+2x^2+x+4\qquad\text{combine like terms}\\\\=2x^2+\left(-\dfrac{1}{2}x+x\right)+\left(\dfrac{1}{3}+4\right)\\\\=2x^2+\dfrac{1}{2}x+4\dfrac{1}{3}$