Study Notes
Functions are mathematical expressions that relate inputs to outputs, often using function notation like f(x). Functions can be evaluated by substituting values into the expression, and composite functions involve substituting one function into another. Reciprocal functions have unique properties such as asymptotes and specific domain and range restrictions.
Exam Tips
Key Definitions to Remember
- Function Notation — A way to write functions, commonly as f(x), which is read as "f of x".
- Composite Function — A function created by substituting one function into another, denoted as f(g(x)).
- Reciprocal Function — A function of the form 1/f(x), with specific domain restrictions.
Common Confusions
- Mistaking f(x) for multiplication of f and x.
- Confusing the inverse of a function with its reciprocal.
Typical Exam Questions
- What is f(4) for f(x) = 3x - 5? Substitute 4 into the function: f(4) = 3(4) - 5 = 7.
- How do you find (f∘g)(x) for f(x) = x^2 + 6 and g(x) = 2x - 1? Substitute g(x) into f(x): (f∘g)(x) = (2x - 1)^2 + 6 = 4x^2 - 4x + 7.
- What is the domain of y = 1/(x+3)? All real numbers except x = -3.
What Examiners Usually Test
- Understanding and using function notation correctly.
- Evaluating functions by substitution.
- Identifying and working with composite functions.
- Determining the domain and range of reciprocal functions.