Table of Contents

- 1 Can a function have 2 ranges?
- 2 How do you find the composition of two functions?
- 3 What is the range of trigonometric functions?
- 4 How do you determine the composition of function?
- 5 Which is the correct way to apply f to a function?
- 6 Is it important to get the domain right when composing a function?

## Can a function have 2 ranges?

Each element of the domain is being traced to one and only element in the range. However, it is okay for two or more values in the domain to share a common value in the range.

### How do you find the composition of two functions?

How to Solve Composite Functions?

- Write the composition in another form. The composition written in the form (f∘g)(x) ( f ∘ g ) ( x ) needs to be written as f(g(x)) f ( g ( x ) ) .
- For every occurrence of x in the outside function i.e. f , replace x with the inside function g(x) .
- Simplify the answer obtained.

**What does it mean to compose two functions?**

Given two functions, we can combine them in such a way so that the outputs of one function become the inputs of the other. This action defines a composite function.

**How do you know if a graph represents a function?**

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

## What is the range of trigonometric functions?

Trigonometric Functions

Function | Domain | Range |
---|---|---|

f(x) = sin ( x ) | (-∞ , + ∞) | [-1 , 1] |

f(x) = cos ( x ) | (-∞ , + ∞) | [-1 , 1] |

f(x) = tan ( x ) | All real numbers except π/2 + n*π | (-in , + ∞) |

f(x) = sec ( x ) | All real numbers except π/2 + n*π | (-∞ , -1] U [1 , + ∞) |

### How do you determine the composition of function?

Summary

- “Function Composition” is applying one function to the results of another.
- (g º f)(x) = g(f(x)), first apply f(), then apply g()
- We must also respect the domain of the first function.

**What does an open circle mean in functions?**

composition operator

The open circle symbol ∘ is called the composition operator. Composition is a binary operation that takes two functions and forms a new function, much as addition or multiplication takes two numbers and gives a new number.

Sal explains what it means to compose two functions. He gives examples for finding the values of composite functions given the equations, the graphs, or tables of values of the two composed functions. Created by Sal Khan. This is the currently selected item. Posted 5 years ago.

**What happens when you combine two domains with a function?**

When you combine the two domains to see what they have in common, you find the intersection of everything and nothing is nothing (the empty set), so the function is defined nowhere and undefined everywhere. When you find (g o f) (x), there are two things that must be satisfied: x must be in the domain of f, which means that x ≥ 4 (not too bad)

## Which is the correct way to apply f to a function?

First we apply f, then apply f to that result: It has been easy so far, but now we must consider the Domains of the functions. The domain is the set of all the values that go into a function. The function must work for all values we give it, so it is up to us to make sure we get the domain correct!

### Is it important to get the domain right when composing a function?

It is important to get the Domain right, or we will get bad results! We must get both Domains right (the composed function and the first function used). When doing, for example, (g º f) (x) = g (f (x)): Now, “x” normally has the Domain of all Real Numbers