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Composition of Functions
Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
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Composition of Functions
What is it?
Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
In simple words
- Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
- Worked pattern: If f(x)=x+2 and g(x)=x^2, then (f o g)(x)=x^2+2.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Composition of functions: Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
What you should learn
- State the rule for composition of functions.
- Solve a composition of functions problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
CONCEPT AND RULE
Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
METHOD
For composition of functions, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
If f(x)=x+2 and g(x)=x2, then (f o g)(x)=x2+2.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve composition of functions
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Composition of functions
- rule
- worked example
- worked example
How the ideas connect
Worked example: If f(x)=x+2 and g(x)=x^2, then (f o g)(x)=x^2+2.
Deeper understanding
Go beyond memorising Composition of Functions. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: If f(x)=x+2 and g(x)=x^2, then (f o g)(x)=x^2+2.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Composition of functions
- rule
- worked example
- Composition of functions: Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
- CONCEPT AND RULE: Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
- METHOD: For composition of functions, identify the given information and required result. Select the matchin
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Composition of Functions: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Composition of functions
- rule
- worked example
- Composition of functions: Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
Important formulas
- Composition of functions
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Composition of functions
rule
worked example
Composition of functions: Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
- Definition
- Composition means (f o g)(x)=f(g(x)); find the inner output first and check both domains.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Composition of Functions.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Composition of Functions and say why it fits.
Mistake
Q4. State one common mistake students make about Composition of Functions.
Exam note
Q5. Write a short exam note on Composition of Functions: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.