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Flip to reveal answersWhat does an inverse function do?
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All 10 Flashcards — Inverse as reflection
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Question
What does an inverse function do?
Answer
It undoes f: if f(a) = b then f⁻¹(b) = a. Inputs and outputs swap.
Question
Is f⁻¹(x) the same as 1/f(x)?
Answer
No — f⁻¹ is the inverse function (reverses f), not the reciprocal.
Question
The graph of f⁻¹ is f reflected in which line?
Answer
y = x. Each point (a, b) on f becomes (b, a) on f⁻¹.
Question
How do you find f⁻¹ algebraically?
Answer
Write y = f(x), swap x and y, then solve for y — that's f⁻¹(x).
Question
Find the inverse of f(x) = 2x + 3.
Answer
Swap: x = 2y + 3 ⇒ y = (x − 3)/2, so f⁻¹(x) = (x − 3)/2.
Question
How do domain and range change for f⁻¹?
Answer
They swap: domain of f⁻¹ = range of f; range of f⁻¹ = domain of f.
Question
Where do f and f⁻¹ intersect?
Answer
On the line y = x — solve f(x) = x to find where.
Question
How can you check an inverse?
Answer
Pick a point: f(a) = b should give f⁻¹(b) = a. Or check f(f⁻¹(x)) = x.
Question
Why might f⁻¹ need a restricted domain?
Answer
Its domain is f's range, which can be limited (e.g. √x has range y ≥ 0, so its inverse x² is restricted to x ≥ 0).
Question
What happens to a point already on y = x under reflection?
Answer
It maps to itself — which is why f and f⁻¹ meet on y = x.
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Full study notes for Inverse as reflection
Topic 2.2 hub
Functions, domain & range
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