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Function Notation

Function Notation problems use custom symbols to represent mathematical functions (e.g., f(x) = x + 3). You must evaluate the function at given input values, often involving multiple functions or compositions.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Function Notation

Function Notation problems use custom symbols to represent mathematical functions (e.g., f(x) = x + 3). You must evaluate the function at given input values, often involving multiple functions or compositions.

Prerequisites

Function concept (input → output) Algebraic substitution Basic algebraic expressions Order of operations
Why This Matters: Function Notation problems appear in 2-3 questions in SSC CGL and Banking PO exams. They test understanding of function concepts and substitution skills.

How to Solve Function Notation Problems

1

Step 1: Identify the function definition (e.g., f(x) = x + 3 means f of x equals x plus 3)

2

Step 2: Locate the input value inside the function notation (e.g., f(5) means input 5)

3

Step 3: Replace every 'x' in the function definition with the input value

4

Step 4: Simplify the resulting expression using order of operations

5

Step 5: For composite functions (f(g(x))), evaluate the innermost function first

6

Step 6: Write the final answer

Pro Strategy: Always work from the innermost function outward. Write each step clearly. For nested functions, evaluate one level at a time.

Example Problem

Example: If f(x) = 2x + 1 and g(x) = x - 3, find f(g(5)). Solution: Step 1: f(x) = 2x + 1, g(x) = x - 3 Step 2: Evaluate innermost first: g(5) = 5 - 3 = 2 Step 3: Now evaluate f(2): f(2) = 2 × 2 + 1 = 4 + 1 = 5 Answer: 5

Pro Tips & Tricks

  • Write the function definition clearly before substituting
  • For composite functions, use parentheses to show nesting: f(g(x))
  • Evaluate the innermost function first, then work outward
  • Check if the function involves special operations (squares, square roots, absolute value)
  • Be careful with negative inputs - use parentheses when substituting
  • For functions with multiple variables, identify which variable is being replaced

Shortcut Methods to Solve Faster

f(a) = replace x with a in the function definition
f(g(a)) = first find g(a), then plug into f
For linear functions, composition is also linear
If f(x) = ax + b, then f(f(x)) = a(ax + b) + b = a²x + ab + b

Common Mistakes to Avoid

Evaluating in wrong order (outside-in instead of inside-out)
Forgetting to substitute all occurrences of the variable
Mixing up which function is applied first in composition
Algebraic errors in simplification

Exam Importance

Function Notation is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
2-3 questions
BANKING PO
2-3 questions
RAILWAYS RRB
2-3 questions
CAT
1-2 questions
INSURANCE
2-3 questions

Ready to Master Function Notation?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now