Question

Which of the following functions has an inverse that is not a function?

y = 2 x + 1
y = x²
y = x

Answer 1

To determine which of the given functions has an inverse that is not a function, we need to determine if each function is one-to-one.

Step-by-step explanation:

In order for a function to have an inverse, it must be a one-to-one function. A one-to-one function means that each unique input value maps to a unique output value. Looking at the given functions:

1. y = 2x + 1: This is a linear function, and it is a one-to-one function. So, it has an inverse that is a function.
2. y = x²: This is a quadratic function, and it is not a one-to-one function because multiple input values can have the same output value. So, it does not have an inverse that is a function.
3. y = x: This is a linear function, and it is a one-to-one function. So, it has an inverse that is a function.

Therefore, the function y = x² has an inverse that is not a function.

Answer 2

y=x^2 has an inverse but it is not a function

Step-by-step explanation:

y = x

y=x has an inverse function. y=x is the equation of a line. All line has an inverse function and it is also a function

y = 2x + 1 is the equation of a line.

All line has an inverse function and it is also a function

y = x^2 is the equation of a quadratic Quadratic equation has an inverse but it does not pass vertical line test.Hence it is not a function

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