Core Mathematics 3: Functions

Core Mathematics 3: Functions

1. A function is a special mapping such that every element of the domain is mapped to exactly one element in the range.

2. A one-to-one function is a special function where every element of the range has been mapped from exactly one element of the domain.

3. Many mappings can be made into functions by changing the domain. For example, the mapping "positive square root" can be changed into the function f(x)= sqrtx by having a domain of x>0

4. If we combine two or more functions we can create a composite function. The function below is written fg(x) as g acts on x first, then f acts as a result. For Example: g(x)=2x+3 f(x)=4x fg(x)=2(4x)+3

5. The inverse of a function f(x) is written as f-1(x) and performs the opposite operation(s) to the function. To calculate the inverse function you change the subject of the formula.

6. The range of the function is the domain of the inverse function and vice versa.

7. The graph of f-1(x) is a reflection of f(x) in the line y=x.