3. Functions

Function Operations

3. Functions

# Function Operations - Video Tutorials & Practice Problems

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concept

## Adding & Subtracting Functions

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example

## Adding & Subtracting Functions Example 1

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concept

## Multiplying & Dividing Functions

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Problem

ProblemGiven the functions $h\left(x\right)=2x^3-4$ and $k\left(x\right)=x^2+2$, find and fully simplify $h\cdot k\left(x\right)$

A

$h\cdot k\left(x\right)=2\left(x^5+2x^3-2x^2-4\right)$

B

$h\cdot k\left(x\right)=2x^5-8$

C

$h\cdot k\left(x\right)=2x^5+4x^3-8$

D

$h\cdot k\left(x\right)=x^2+4x+4$

5

Problem

ProblemGiven the functions $L\left(x\right)=x-2$ and $M\left(x\right)=x^2$, calculate $\frac{L}{M}\left(5\right)$

A

$\frac{L}{M}\left(5\right)=\frac{25}{3}$

B

$\frac{L}{M}\left(5\right)=\frac53$

C

$\frac{L}{M}\left(5\right)=\frac{3}{25}$

D

$\frac{L}{M}\left(5\right)=\frac35$

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PRACTICE PROBLEMS AND ACTIVITIES (51)

- Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 ...
- Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 ...
- In Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15
- Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)
- Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(-1)
- In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]
- Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)
- For the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8
- For the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-5
- For the pair of functions defined, find (ƒ-g)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x...
- For the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1...
- In Exercises 1–30, find the domain of each function. h(x) = √(x −2)+ √(x +3)
- In Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²
- Use the graph to evaluate each expression. See Example 3(a). (ƒ+g)(2)
- In Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²
- Use the graph to evaluate each expression. See Example 3(a). (ƒ-g)(-1)
- In Exercises 31–50, find ƒ/g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1
- In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1
- In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15
- In Exercises 31–50, find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4
- In Exercises 31–50, find f/g and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x
- For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=2-x
- In Exercises 31–50, find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)
- In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)
- For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1/x
- In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) =...
- For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2
- For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1+2x^2
- In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2
- For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2-4x+2
- In Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5
- Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘ƒ)(0)
- Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘g)(-2)
- In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 1/x, g(x)= 1/x
- Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1
- Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3
- In Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog...
- Given functions f and g, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x^3, g(x)=x^2+3x-1
- Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4
- Given functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x
- Use the graphs of f and g to solve Exercises 83–90. Find (g-f) (-2).
- Given functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=1/(x+5)
- In Exercises 87–88, find a. (f ○ g)(x); b. the domain of (f ○ g). f(x) = (x + 1)/(x - 2), g(x) = 1/x
- Use the graphs of f and g to solve Exercises 83–90. Graph f+g.
- Use the graphs of f and g to solve Exercises 83–90. Graph f-g.
- Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(x)
- Let ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(3)
- Use the table to evaluate each expression, if possible. (ƒ+g)(1)
- Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4
- Use the table to evaluate each expression, if possible. (f/g) (0)
- The graphs of two functions ƒ and g are shown in the figures. Find (ƒ∘g)(2).