Inverse functions
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Flip to reveal answersWhat does the inverse function f⁻¹ do?
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All 8 Flashcards — Inverse functions
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Question
What does the inverse function f⁻¹ do?
Answer
It undoes f: if f maps a→b, then f⁻¹ maps b→a. So f⁻¹(f(x)) = x.
Question
How do you find f⁻¹ algebraically?
Answer
Write y = f(x), swap x and y, then solve for y.
Question
What does f⁻¹(b) mean numerically?
Answer
The input that gives output b — i.e. solve f(x) = b.
Question
Is f⁻¹ the same as 1/f?
Answer
No — f⁻¹ is the inverse function (reverses f); 1/f is the reciprocal.
Question
How are the graphs of f and f⁻¹ related?
Answer
f⁻¹ is the reflection of f in the line y = x; each (a,b) becomes (b,a).
Question
When does an inverse function exist?
Answer
Only when f is one-to-one (passes a horizontal line test); otherwise restrict the domain.
Question
How do domain and range change for the inverse?
Answer
They swap: the range of f becomes the domain of f⁻¹.
Question
Find f⁻¹ for f(x) = 4x + 3.
Answer
y = 4x+3 → x = 4y+3 → f⁻¹(x) = (x−3)/4.
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Full study notes for Inverse functions
Topic 2.7 hub
Composite & inverse functions (HL only)
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