Question

F: Z → Z. f(x) = x + 3 Select the correct description of the function f

a. One-to-one and onto
b. One-to-one but not onto
c. Onto but not one-to-one
d. Neither one-to-one nor onto

Answer 1

The function f(x) = x + 3 is one-to-one and onto.

Step-by-step explanation:

The function f(x) = x + 3 is a linear function that maps every integer to another integer. To determine if this function is one-to-one, we need to check if each input value has a unique output value. In this case, if we consider two different input values x and y, we can see that f(x) will be equal to f(y) only if x + 3 = y + 3, which implies x = y. Therefore, the function f is one-to-one.

To determine if the function is onto, we need to check if every integer can be obtained as an output. In this case, let's consider an arbitrary integer y. If we choose x = y - 3 as the input value, then f(x) = (y - 3) + 3 = y. This shows that every integer can be obtained as an output, so the function f is onto. Therefore, the correct description of the function f is One-to-one and onto (option a).