Math basics › Precalculus
Composing functions
Inside first
f(g(x)) means put x into g, then take whatever comes out and put it into f. Work from the inside out, the way you would with brackets.
Order changes everything
f(g(x)) and g(f(x)) are almost never the same function. If you square then add one you get x² + 1; add one then square and you get (x + 1)².
The domain can shrink
The inside function has to be allowed to produce what the outside function can take. √(x) inside ln() means x has to be positive, not just non-negative.