Which of the following functions has an inverse that is not a function?
y=x
y=2x+1
y=x to the second power
Hint: Use the horizontal test:
If you draw a horizontal line through the function, and it is possible to intersect the function at more than one point, then the inverse is not a function.
To determine which of the given functions has an inverse that is not a function, we need to check if each function satisfies the criteria for having an inverse.
A function has an inverse if and only if it is one-to-one or injective, meaning that each input value corresponds to a unique output value.
Let's analyze each given function:
1. y = x
This function is a linear function with a slope of 1, meaning each input value has a unique corresponding output value. Therefore, it is one-to-one and has an inverse that is a function.
2. y = 2x + 1
This function is also a linear function with a slope of 2, which means that each input value has a unique corresponding output value. It is one-to-one and has an inverse that is a function.
3. y = x^2
This function is a quadratic function, and unlike the linear functions above, it fails the one-to-one criterion. For example, both x = 2 and x = -2 result in y = 4. Therefore, this function does not have an inverse that is a function.
Thus, the given functions "y=x" and "y=2x+1" have inverses that are functions, while the function "y=x^2" does not.