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Example of a function that has no inverse function? - Answers

y = sin x is such a function. It has an inverse, of course; but the inverse, sin-1, strictly speaking, is not a function.Example: Given that x = pi/6, y must equal 0.5. However, given that y = 0.5, x can equal pi/6, 5 pi/6, 13 pi/6, 17 pi/6, or an infinity of values, both positive and negative.For y to be a function of x, and x to be, also, a function of y, there must be exactly one value of y that answers to a given value of x, and vice-versa. Then, and only then, is each function the inverse of the other.



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Example of a function that has no inverse function? - Answers

https://math.answers.com/other-math/Example_of_a_function_that_has_no_inverse_function

y = sin x is such a function. It has an inverse, of course; but the inverse, sin-1, strictly speaking, is not a function.Example: Given that x = pi/6, y must equal 0.5. However, given that y = 0.5, x can equal pi/6, 5 pi/6, 13 pi/6, 17 pi/6, or an infinity of values, both positive and negative.For y to be a function of x, and x to be, also, a function of y, there must be exactly one value of y that answers to a given value of x, and vice-versa. Then, and only then, is each function the inverse of the other.



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https://math.answers.com/other-math/Example_of_a_function_that_has_no_inverse_function

Example of a function that has no inverse function? - Answers

y = sin x is such a function. It has an inverse, of course; but the inverse, sin-1, strictly speaking, is not a function.Example: Given that x = pi/6, y must equal 0.5. However, given that y = 0.5, x can equal pi/6, 5 pi/6, 13 pi/6, 17 pi/6, or an infinity of values, both positive and negative.For y to be a function of x, and x to be, also, a function of y, there must be exactly one value of y that answers to a given value of x, and vice-versa. Then, and only then, is each function the inverse of the other.

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      y = sin x is such a function. It has an inverse, of course; but the inverse, sin-1, strictly speaking, is not a function.Example: Given that x = pi/6, y must equal 0.5. However, given that y = 0.5, x can equal pi/6, 5 pi/6, 13 pi/6, 17 pi/6, or an infinity of values, both positive and negative.For y to be a function of x, and x to be, also, a function of y, there must be exactly one value of y that answers to a given value of x, and vice-versa. Then, and only then, is each function the inverse of the other.

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