Answer:
d(x) = x³ - 1
Explanation:
Definition of a one-to-one function
A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f . In other words, each x in the domain has exactly one value of f(x)
If the graph of a function f is known, it is easy to determine if the function is 1 -to- 1 we can use the horizontal line test. If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 .
Quadratic and absolute functions have the same y value for multiple values of x. So they are not one-to one. So t(x) and g(x) are not one-to-one
Cubic functions of the form ax³ + bx + c are one-to-one. However, if it has a quadratic component and the form is ax³ + bx² + cx + d then it will not be one to one. So p(x) is not one-to-one.
The only one-to-one function is d(x) = x³ - 1 which has a unique y value for any value of x
Graphs with horizontal line test support this choice