Final answer:
The function f(x) = x² - 6x - 55 is not one-to-one because two different inputs, x = 11 and x = -5, give the same output of 0. This can be determined by finding two x-values that result in the same f(x)-value, violating the definition of a one-to-one function.
Step-by-step explanation:
To show that the given function f(x) = x² - 6x - 55 is not one-to-one, we need to find at least two different values of x that give us the same value of f(x). One way to finding whether a function is one-to-one or not is by using the Horizontal Line Test. If any horizontal line cuts the graph of the function at more than one point, it indicates that the function is not one-to-one because it gives the same output for multiple inputs.
Let's see what happens when we plug different values of x into our function:
- f(11) = 11² - 6(11) - 55 = 121 - 66 - 55 = 0
- f(-5) = (-5)² - 6(-5) - 55 = 25 + 30 - 55 = 0
Here, we have two different inputs, x = 11 and x = -5, that give the same output, which is 0. Therefore, f(x) is not one-to-one since it assigns the same function value to more than one element in its domain.