Answer:
f(x) = x^2
Explanation:
A function that does not have an inverse function is called a non-invertible or many-to-one function. An example of a non-invertible function is:
f(x) = x^2
To determine if a function is invertible, we need to check if it passes the horizontal line test. If a horizontal line intersects the graph of the function at more than one point, then the function is not invertible.
For the function f(x) = x^2, if we draw a horizontal line at any value of y, it will intersect the graph of the function at two points, one on the positive x-axis and the other on the negative x-axis.
Therefore, f(x) is not invertible, as it fails the horizontal line test.
In other words, there are multiple x-values that correspond to a single y-value. For example, both x = 2 and x = -2 have the same y-value of 4. As a result, there is no unique inverse function that could map a value of 4 back to a single x-value.
In conclusion, the function f(x) = x^2 is an example of a non-invertible function, as it fails the horizontal line test and does not have a unique inverse function.