3. Functions

Function Operations

Open Question
Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4
Multiple Choice
Given the functions $h\left(x\right)=2x^3-4$ and $k\left(x\right)=x^2+2$ , find and fully simplify $h\cdot k\left(x\right)$
Multiple Choice
Given the functions $L\left(x\right)=x-2$ and $M\left(x\right)=x^2$ , calculate $\frac{L}{M}\left(5\right)$
Open Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ+g)(2)
Open Question
Without using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2(ƒ/g)(2)
Open Question
In Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15
Open Question
Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)
Open Question
Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(-1)
Open Question
In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]
Open Question
Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)
Open Question
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
Open Question
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
Open Question
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^2-x+3
Open Question
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/x
Open Question
In Exercises 1–30, find the domain of each function. h(x) = √(x −2)+ √(x +3)