Inverses: domain restriction & self-inverse
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Flip to reveal answersWhen does a function have an inverse?
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All 8 Flashcards — Inverses: domain restriction & self-inverse
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Question
When does a function have an inverse?
Answer
When it's one-to-one (each output comes from exactly one input — passes the horizontal-line test).
Question
What do you do if a function isn't one-to-one?
Answer
Restrict its domain to a stretch where it IS one-to-one, then invert.
Question
How do you find an inverse algebraically?
Answer
Write y = f(x), make x the subject, then swap x and y.
Question
What is a self-inverse function?
Answer
One that is its own inverse: f(f(x)) = x, so f⁻¹ = f; its graph is symmetric in y = x.
Question
Two classic self-inverse functions?
Answer
f(x) = 1/x and f(x) = a − x.
Question
How are the domain and range of f related to f⁻¹?
Answer
The domain of f⁻¹ is the range of f, and the range of f⁻¹ is the domain of f.
Question
Largest domain for cos x to have an inverse?
Answer
[0, π] — where cos is one-to-one (the arccos domain).
Question
Restrict x² so it has an inverse — what's f⁻¹?
Answer
On x ≥ 0, f⁻¹(x) = √x.
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Full study notes for Inverses: domain restriction & self-inverse
Topic 2.14 hub
Odd, even & self-inverse (HL only)
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