Let $f$ be a monotonic function $f:[a,b] \rightarrow\mathbb{R}$ and $g$ be a monotonic function $g:[c,d]\rightarrow[a,b]$. Show that $f\circ g$ is monotonic
Asked
Active
Viewed 3,467 times
1
-
1What are your thoughts on the question? What have you tried so far? – Ben Grossmann Apr 22 '15 at 15:21
1 Answers
3
Let $*$ represent either $<$ or $>$, depending on the direction of the monotonicity in each case. Then $$x*y\implies g(x)*g(y)\implies f\circ g(x)*f\circ g(y)$$
ajotatxe
- 65,084
-
I'm sorry, I'm a bit confused here. What does ∗ really represent? Is it a function's operator? – user233580 Apr 22 '15 at 15:35
-
2As I said it is either "lesser than" or "greater than". (This notation is not standard at all). – ajotatxe Apr 22 '15 at 16:19