Function
Gujarat Board · Class 11 · Statistics
Quick revision notes for Function — Gujarat Board Class 11 Statistics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Definition and Basic Concepts of Functions
- A function is a unique relation between elements of two non-empty sets where each element of the first set has exactly one image in the second set
- For a relation to be a function, every element in the domain must have exactly one corresponding element in the codomain
- Functions are denoted by letters like f, g, h, and written as f: A → B
Types of Functions - Detailed Analysis
- One-One Function: Different inputs give different outputs (f(a₁) ≠ f(a₂) when a₁ ≠ a₂)
- Many-One Function: Different inputs can give the same output (f(a₁) = f(a₂) when a₁ ≠ a₂)
- Constant Function: All inputs give the same output (f(x) = c for all x in domain)
Equal Functions and Function Comparison
- Two functions are equal if they have the same domain and same functional values for every element
- Domain equality is necessary but not sufficient for function equality
- Equal functions must satisfy: f = g if Domain(f) = Domain(g) and f(x) = g(x) for all x in domain
Real Functions and Function Evaluation
- Real functions have domain and/or codomain as subsets of real numbers
- Function evaluation involves substituting values and simplifying expressions
- Domain restrictions occur when denominators become zero or expressions under square roots become negative
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Function covers several key topics that are frequently asked in Gujarat Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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