Question

Which function has an inverse that is also a function?

a) g(x) = -2x^3
b) k(x) = -9x^2
c) f(x) = |x + 2|
d) w(x) = -20

Answer 1

The function that has an inverse that is also a function is f(x) = |x + 2|.

Step-by-step explanation:

A function has an inverse that is also a function if it is one-to-one. This means that each element in the domain corresponds to a unique element in the range, and vice versa. To determine which function has an inverse that is also a function, we can analyze the options:

• a) g(x) = -2x^3: This function is not one-to-one because multiple values of x can map to the same value of y.
• b) k(x) = -9x^2: This function is also not one-to-one because multiple values of x can map to the same value of y.
• c) f(x) = |x + 2|: This function is one-to-one because each value of x maps to a unique value of y. Therefore, option c) has an inverse that is also a function.
• d) w(x) = -20: This function is a constant, so it is not one-to-one and does not have an inverse that is also a function.