Question

Funtion Definitions
*Need editor hold on*

Answer 1

If you define the folowing functions as such:
\[f:[0,\infty )\rightarrow [0,\infty )\quad f\left( x \right) :=\sqrt { x } \\ g:[0,\infty )\rightarrow { R }\quad g\left( x \right) :=\sqrt { x }\]
Is the composite \( f\circ g\) properly defined?

I would think it is NOT as g(x) maps to all Real numbers, while the domain of f(x) is \([0,\infty)\).

Answer 2

R is codomain for the second function
it maps to the Range which is [0,infinity)

Answer 3

its defined just fine

Answer 4

Ah, codomain not the range.

Answer 5

\[\sqrt{x}\ge0\]
so
\[\sqrt{\sqrt{x}}\] is fine

Answer 6

@zzr0ck3r Thanks, codomain always confuses me. But I got it now.

Answer 7

codomain is what you are allowed to map to, range is what you map to