Let f and g be decreasing functions forall real numbers. prove
that f o g isincreasing.

Proof with Step-by-step explanation:

Since it is given that f(x) is decreasing thus we infer that

Similarly it is given that g(x) is decreasing thus we infer that

Now let

Differentiating both sides with respect to 'x' and using chain rule of differentiation we get

Now since both f'(x) and g'(x) are both negative(<0) we can infer that their product is always positive (>0)

Thus fog(x) is an increasing function.