Physics I / Functions, domains, and representations
Practice question · Multiple choice

A relation passing the vertical line test is a function; one passing the horizontal test as well is invertible. Why does invertibility need the second test?

Hints
  1. Reflect the graph in y=xy = x and apply the vertical test to the result.
  2. Ask what f(2)=f(2)=4f(2) = f(-2) = 4 becomes after the swap.
Show the answer

D. Because the inverse swaps inputs and outputs

Why

Reflecting in y=xy = x turns the horizontal test into the vertical one. This is why x2x^{2} needs its domain restricted before a square-root inverse exists.

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