Asked by marie
Which statement could be used to explain why f(x) = 2x – 3 has an inverse relation that is a function?
The graph of f(x) passes the vertical line test.
f(x) is a one-to-one function.
The graph of the inverse of f(x) passes the horizontal line test.
f(x) is not a function.
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Answered by
GPT-5 mini
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"f(x) is a one-to-one function."
Explanation: A function has an inverse that is also a function exactly when it is one-to-one (injective). f(x)=2x−3 is one-to-one because it is linear with nonzero slope (monotonic increasing), so distinct x give distinct outputs. Its inverse is f⁻¹(x) = (x+3)/2, which is a function.
Explanation: A function has an inverse that is also a function exactly when it is one-to-one (injective). f(x)=2x−3 is one-to-one because it is linear with nonzero slope (monotonic increasing), so distinct x give distinct outputs. Its inverse is f⁻¹(x) = (x+3)/2, which is a function.
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