Intermediate Algebra, Chapter 5, 5.3, Section 5.3, Problem 14

If $f(x) = -4x + 1$ and $g(x) = 6x + 2$. Find (a) $(f + g)(x)$ (b) $(f - g)(x)$
a.) For $(f + g)(x)$

Compose the result function for $f+g$ by replacing the function designators with the actual functions.

$(1−4x)+(6x+2)$


Remove the parentheses that are not needed from the expression.

$1−4x+6x+2$


Add 2 to 1 to get 3.

$3−4x+6x$


Since $−4x$ and $6x$ are like terms, subtract $6x$ from $−4x$ to get $2x$.

3+2x


Reorder the polynomial $3+2x$ alphabetically from left to right, starting with the highest order term.

$(f + g)(x) = 2x+3$

b.) $(f - g)(x)$
Compose the result function for $f−g$ by replacing the function designators with the actual functions.

$(1−4x)−(6x+2)$


Multiply $−1$ by each term inside the parentheses.

$1−4x−6x−2$


Subtract 2 from 1 to get $−1$.

$−1−4x−6x$


Since $−4x$ and $−6x$ are like terms, subtract $6x$ from $−4x$ to get $−10x$.

$−1−10x$


Reorder the polynomial $−1−10x$ alphabetically from left to right, starting with the highest order term.

$(f - g)(x) = −10x−1 $