Composite of decreasing and increasing function [closed]
Since $g(x)$ is decreasing , we know that if $x_1 \leq x_2 \implies g(x_1) \geq g(x_2)$. Since $f(x)$ is increasing we know that $x_1 \leq x_2 \implies f(x_1) \leq f(x_2)$. Now suppose we select that $x_1 \leq x_2$ and want to know the relation between $$ f(g(x_1)), f(g(x_2)). $$
Well since $x_1 \leq x_2$ we know that $g(x_1) \geq g(x_2)$. From here do you think you can finish the problem?