## PhoenixFire 2 years ago Funtion Definitions *Need editor hold on*

1. PhoenixFire

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 $$[0,\infty)$$.

2. zzr0ck3r

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

3. zzr0ck3r

its defined just fine

4. PhoenixFire

Ah, codomain not the range.

5. zzr0ck3r

$\sqrt{x}\ge0$ so $\sqrt{\sqrt{x}}$ is fine

6. PhoenixFire

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

7. zzr0ck3r

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