Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function?

h(x) = x^3

A function has an inverse that is also a function is it is a one-to-one function, a function is one-to-one if each value in the domain is linked to only one value in the range, and if each value in the range is linked to only one value in the domain.

Then, a function that is monotonous growing is always one to one, and a function is monotonous growing if the derivative is positive for all the values of x

The derivative of x^3 is:

h'(x) = 3*x^2

and as you know, x^2 is always equal or greater than zero, so h(x) = x^3 is monotonous growing, then it has a inverse that is also a function.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!