# Section 1.8 – Combinations of Functions

Section Details.
• Finding the sum, difference, product, and quotient of functions
• Finding the composition of functions and its domain

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.

Perform the indicated operation on the functions $$f(x)=3x^2+5$$ and $$g(x)=x+7$$ and determine the domain of each new function.

1. Solve $$(f+g)(x)$$.
2. Solve $$(fg)(x)$$.
3. Solve $$\left(\cfrac{f}{g}\right)(x)$$.
4. Solve $$(f\circ g)(x)$$.

1. $$(f+g)(x)=3x^2+x+12,\quad$$ Domain: $$(-\infty, \infty)$$
2. $$(fg)(x)=3x^2+21x^2+5x+35,\quad$$ Domain: $$(-\infty, \infty)$$
3. $$\left(\dfrac{f}{g}\right)(x)=\dfrac{3x^2+5}{x+7},\quad$$ Domain: $$(-\infty,-7)\cup(-7,\infty)$$
4. $$(f(g(x)))=3x^2+42x+152,\quad$$ Domain: $$(-\infty, \infty)$$

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