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Chatty reference · maths1 week 5

100 words
1 min read
2026-08-16

5. Maths Week 5 — Functions

Official topics include horizontal/vertical line tests, exponential functions, composite functions and inverse functions. citeturn1view0

Concepts

  • Function as mapping
  • Domain
  • Range
  • Vertical line test
  • Horizontal line test
  • One-to-one behaviour
  • Exponential functions
  • Composition
  • Inverse functions
Composition:
(f∘g)(x)=f(g(x))(f\circ g)(x)=f(g(x))
Inverse:
f−1(f(x))=xf^{-1}(f(x))=x

Patterns

  • Is this graph a function?
  • Is this function one-to-one?
  • Compute f(g(x))f(g(x)).
  • Compute g(f(x))g(f(x)).
  • Determine domain restrictions.
  • Find inverse.
  • Verify inverse.
  • Distinguish function from inverse relation.

Classic trap

f(g(x))≠g(f(x))f(g(x))\neq g(f(x))
in general.
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