Find the indicated function value.
-$$f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$$
Find $( f + g ) ( x )$.
A) $x ^ { 3 } + \frac { 1 } { 3 } x ^ { 2 } + \frac { 4 } { 3 } x - 3$
B) $2 x ^ { 3 } - \frac { 1 } { 6 } x ^ { 2 } - 2 x$
C) $x ^ { 3 } + \frac { 1 } { 6 } x ^ { 2 } + \frac { 2 } { 3 } x - 3$
D) $2 x ^ { 3 } - \frac { 1 } { 3 } x ^ { 2 } - 2 x$

Question

Quizplus · Accepted Answer

To find $(f + g)(x)$, add the corresponding terms of $f(x)$ and $g(x)$: $x^2 + \frac{1}{3}x - 3 + x^3 - \frac{2}{3}x^2 + x = x^3 + \left(1 - \frac{2}{3}\right)x^2 + \left(\frac{1}{3} + 1\right)x - 3 = x^3 + \frac{1}{3}x^2 + \frac{4}{3}x - 3$.

Find the Indicated Function Value f(x)=x2+13x−3,g(x)=x3−23x2+xf ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + xf(x)=x2+31​x−3,g(x)=x3−32​x2+x

Find the Indicated Function Value $f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$