$f\ is\ convex\ on\ (a,b),g\ is\ convex\ on\ (c,d),Range\ of\ f \subset\ (c,d),prove\ that\ g(f(x))\ is\ convex\ on\ (a,b). $
The convexity of compound function
0
$\begingroup$
analysis
1 Answers
0
It's not true. Consider for example $f:x\mapsto x^2$ and $g:x\mapsto e^{-x}$.
Both are convex but $x\mapsto e^{-x^2}$ is not convex.