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PhoenixFire
 one year ago
Best ResponseYou've already chosen the best response.0If 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 \([0,\infty)\).

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2R is codomain for the second function it maps to the Range which is [0,infinity)

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2its defined just fine

PhoenixFire
 one year ago
Best ResponseYou've already chosen the best response.0Ah, codomain not the range.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2\[\sqrt{x}\ge0\] so \[\sqrt{\sqrt{x}}\] is fine

PhoenixFire
 one year ago
Best ResponseYou've already chosen the best response.0@zzr0ck3r Thanks, codomain always confuses me. But I got it now.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.2codomain is what you are allowed to map to, range is what you map to
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