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Apply the horizontal or vertical line test to determine if the inverse of the function is a function.

Is the inverse of the function a function?
No
Yes

66. Apply the horizontal or vertical line test to determine if the inverse of the function is a function.\newlineIs the inverse of the function a function?\newlineNo\newlineYes

Full solution

Q. 66. Apply the horizontal or vertical line test to determine if the inverse of the function is a function.\newlineIs the inverse of the function a function?\newlineNo\newlineYes
  1. Understand horizontal line test: Step 11: Understand the horizontal line test.\newlineTo determine if a function has an inverse that is also a function, we use the horizontal line test. If any horizontal line crosses the graph of the function more than once, the inverse is not a function.
  2. Apply horizontal line test: Step 22: Apply the horizontal line test.\newlineAssume the function's graph is given or visualized. If a horizontal line intersects the graph at multiple points, the inverse will not pass the vertical line test, meaning it's not a function.
  3. Conclusion: Step 33: Conclusion based on the test.\newlineSince the horizontal line test fails (as assumed for this problem), the inverse of the function is not a function.

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