TITLE: What does a mini circle between f and h(x) mean?
QUESTION [18 upvotes]: I am currently doing a math problem and have come across an unfamiliar notation.
A mini circle between $f$ and $h(x)$
The question ask me to find for 'the functions $f(x)=2x-1$ and $h(x)=3x+2$'
$$f \circ h(x)$$
However, I can't do this as I do not know what the circle notation denotes to.
Does it mean to multiply?

REPLY [10 votes]: The circle $\circ$ is the symbol for composition of functions. In General, if you have two functions $g\colon X\rightarrow Y$ and $f\colon Y\rightarrow Z$, then
$f\circ g$ is a function from $X$ to $Z$. For $x\in X$ one has $(f\circ g)(x) = f(g(x))$.
In your case one has: $f(x) = 2x-1$, $g(x) = 3x+2$ and 
$$
(f\circ g)(x) = f(g(x)) = 2(g(x))-1 = 2(3x+2) -1 = 6x+3.
$$
You take the function $g(x)$ and put it in place of the $x$ in the function $f$.
This is obviously different from $f(x)\cdot g(x) = (2x-1)\cdot (3x+2) = 6x^2+x-2$.