Functions – General Mathematics Notes
1. Introduction to Functions
- A function is a relation where each input (x) has exactly one output (y).
- Functions are commonly written as f(x), meaning “f of x.”
- Example: f(x) = 2x + 3
- If x = 2, then f(2) = 2(2) + 3 = 7
2. Definition of a Function
- A function is a rule that assigns each element in the domain (input) to
exactly one element in the range (output).
- Notation: f: X → Y, meaning f is a function from set X to set Y.
Example of a function:
F(x) = x^2 + 1
Domain (Input values): {1, 2, 3}
Range (Output values): {2, 5, 10}
3. Domain and Range of a Function
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).
Example:
For f(x) = √(x – 1)
- The domain is x ≥ 1 (because we cannot take the square root of a negative
number).
- The range is y ≥ 0.
1. Introduction to Functions
- A function is a relation where each input (x) has exactly one output (y).
- Functions are commonly written as f(x), meaning “f of x.”
- Example: f(x) = 2x + 3
- If x = 2, then f(2) = 2(2) + 3 = 7
2. Definition of a Function
- A function is a rule that assigns each element in the domain (input) to
exactly one element in the range (output).
- Notation: f: X → Y, meaning f is a function from set X to set Y.
Example of a function:
F(x) = x^2 + 1
Domain (Input values): {1, 2, 3}
Range (Output values): {2, 5, 10}
3. Domain and Range of a Function
- Domain: The set of all possible input values (x-values).
- Range: The set of all possible output values (y-values).
Example:
For f(x) = √(x – 1)
- The domain is x ≥ 1 (because we cannot take the square root of a negative
number).
- The range is y ≥ 0.
