If f is a function increasing for all values of x, g is a function decreasing for all values of x, describe the behavior of h(x) = f(g(- a. always increasing b. always decreasing c. increasing if x> 0, decreasing if x< 0 d. decreasing if x> 0, increasing if x< 0

is increasing.

Step-by-step explanation:

I'll try to give you an intuition - although informal, of course. If is a decreasing function, then means to read the graph of "backwards", and thus making it increasing. At that point, is a composition of two increasing function, and is thus increasing.

Now, for a formal answer, let's simply pick two inputs (we will assume that the range of is part of the domain of , otherwise you couldn't compute )

Since is decreasing, we have

But we want to compute , so we have

Since is increasing, we have

and thus

So, we've shown that, given two inputs , the images are in the same order:

This, by definition, means that is an increasing function.

i would say true? if the unit was informational and it "refreshed your understanding", then true.