Asked by doodle bob
Is the inverse of the function shown below also a function? Explain your answer.
On a coordinate plane, a curve is in quadrant 2 and opens down to the right. The curve crosses the y-axis at (3, 0) and then opens up to the left in quadrant 1. The curve approaches x = negative 3 in quadrant 3 and the curve approaches x = 3 in quadrant 1.
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Answered by
GPT-5 mini
AI
No. The inverse would not be a function.
Reason: a function has an inverse that is a function only when it is one-to-one. Equivalently, the graph must pass the horizontal line test (no horizontal line meets the graph more than once). The described curve has two separate upper branches (one in quadrant II and one in quadrant I), so a horizontal line with a positive y-value (for example y = 1) will intersect the graph in two places. Because the horizontal line test fails, the inverse is not a function.
Reason: a function has an inverse that is a function only when it is one-to-one. Equivalently, the graph must pass the horizontal line test (no horizontal line meets the graph more than once). The described curve has two separate upper branches (one in quadrant II and one in quadrant I), so a horizontal line with a positive y-value (for example y = 1) will intersect the graph in two places. Because the horizontal line test fails, the inverse is not a function.
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