A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

Step-by-step explanation:

A). If a function 'f' is inverse of another function 'g',

Then f[g(x)] = x = g[f(x)]

In this question the given functions are,

f(x) = and g(x) =

Then, f[g(x)] =

                    =

                    = x

Similarly, g[f(x)] =

                         =

                         = x

Therefore, Both the functions are inverse of each other.

B). Domain of the compositions of these functions will be a set of all real numbers, (-∞, ∞)

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it