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17
g(2)=6; f(6)=17.
Class 10 · English Version · Mathematics
Equations, patterns and functions
Interpret function composition, inverses and graph transformations.
About this lesson and its coverage
Original Kidemy Class 10 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
Composition applies the inside function first. An inverse reverses a function only on a domain where outputs identify inputs uniquely. A horizontal shift inside brackets has the opposite apparent sign to a coordinate change.
Worked example
If f(x)=2x+3 and g(x)=x², f(g(2))=11 while g(f(2))=49. The inverse of f is (x−3)/2.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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9
f(2)=5; g(5)=9.
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5
The squared term vanishes at 5.
Write in your own words. A guardian or teacher should review this response.
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f⁻¹(x)=(x+7)/4.
Reverse subtraction and multiplication.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
Without restriction, x and −x have the same square, so the output does not identify one input.
Explain one-to-one behaviour.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Compare f∘g and g∘f with a table and verify an inverse by composition.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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