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.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12