Use the definition of a one-to-one function to determine if the function is one-to-one.
$q (x) = x^{3} - 17$

The function is one-to-one.
The function is not one-to-one.

Answer

Expert–verified

Hide Steps

Answer

$The function is one-to-one.$

Steps

Step 1 ：Use the definition of a one-to-one function to determine if the function is one-to-one.

Step 2 ：To determine if a function is one-to-one, we need to check if every output value corresponds to exactly one input value.

Step 3 ：For any two different input values, the output values must also be different.

Step 4 ：For the given function $q (x) = x^{3} - 17$ , we can use the fact that the cube function $x^{3}$ is a one-to-one function.

Step 5 ：Subtracting 17 from $x^{3}$ does not change the one-to-one property of the function.

Step 6 ： $The function is one-to-one.$