Intermediate Algebra, Chapter 5, 5.3, Section 5.3, Problem 13

If $f(x) = 5x - 10$ and $g(x) = 3x + 7$. 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.

$(5x−10)+(3x+7)$


Remove the parentheses that are not needed from the expression.

$5x−10+3x+7$


Since $5x$ and $3x$ are like terms, add $3x$ to $5x$ to get $8x$.

$8x−10+7$


Add $7$ to $−10$ to get $−3$.

$(f+g)(x) = 8x−3$
b.) For $(f - g)(x)$


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

$(5x−10)−(3x+7)$


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

$5x−10−3x−7$


Since $5x$ and $−3x$ are like terms, add $−3x$ to $5x$ to get $2x$.

$2x−10−7$


Subtract $7$ from $−10$ to get $−17$.

$(f - g)(x) = 2x−17$