1. Tricky question

Morning Forum I am having issues with the following question any help would be appreciated:

2. Originally Posted by AlgebraicallyChallenged
Morning Forum I am having issues with the following question any help would be appreciated:
It might help if you write

$\displaystyle f\circ g(x)$ as $\displaystyle f(g(x))$

and

$\displaystyle g \circ f(x)$ as $\displaystyle g(f(x))$.

Can you see what's happening now?

3. I can't remember how is that sign called between the f and g..
$\displaystyle f\circ g(x)$

compo.. something?

4. Originally Posted by metlx
I can't remember how is that sign called between the f and g..
$\displaystyle f\circ g(x)$

compo.. something?
Yes it's a composition of functions.

Let me put it this way.

Say you had a function $\displaystyle f(x)$.

If you evaluated it at say, point $\displaystyle x = a$ you would have to replace all the x's with a's.

Here, if we had $\displaystyle f \circ g(x) = f(g(x))$, instead of substituting x with a, we'd see what happens if we replaced all the x's with whatever $\displaystyle g(x)$ is.

Does that make sense?