Functions Functions - Notation, Domain, Range, Composite and Inverse

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.

About the author

Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

We write f(x) for the output. If f(x) = 2x + 3 then f(4) = 11. One input, one output - always.

Watch for traps: under a root must be ≥ 0, and you can never divide by 0. These set the domain.

Work right to left: g is nearest x, so g goes first. Usually fg ≠ gf - order matters.

Write y = f(x), swap x and y, then make y the subject. The graph reflects in the line y = x.

function	a rule giving exactly one output for each input, written f(x)
domain	the set of all allowed input values of a function
range	the set of all possible output values of a function
composite function	a function made by feeding one function's output into another; fg(x) = f(g(x))
inverse function	the function that undoes f; if f(a) = b then f⁻¹(b) = a
one-to-one	each output comes from exactly one input; required for an inverse
substitute	replace the variable x with a given number or expression
commutative	an operation whose order does not change the result

🔒

You have read the summary. The board-ready model answers, grammar notes, one-touch audio and writing practice for this chapter are part of Lipi©.

See it, understand it, hear it read aloud, then write the exam answer with confidence, for a fraction of a tutor cost.