Answer with Step-by-step explanation:
We are given that two functions f and g are decreasing function for all real numbers .
We have to prove that fog is increasing.
Increasing Function: If [tex]x_1 \leq x_2[/tex]
Then, [tex]f(x_1)\leq f(x_2)[/tex]
Decreasing function: if [tex]x_1\leq x_2[/tex]
Then, [tex]f(x_1)\geq f(x_2)[/tex]
Suppose [tex]f(x)=-x[/tex]
[tex]g(x)=-2x[/tex]
fog(x)=f(g(x))=f(-2x)=-(-2x)=2x
Therefore, f and g are decreasing function for all real numbers then fog is increasing.
Hence, proved
