Answer:
All Real x larger or equal zero
or in inequality form: [tex]x\geq 0[/tex]
or in interval notation: [tex][0,\infty)[/tex]
Step-by-step explanation:
If [tex]f(x)=2x[/tex] and [tex]g(x)=\sqrt{x}[/tex], then using the definition for the composition of functions [tex](fo\,g)(x)=f(g(x))[/tex], we get:
[tex](fo\,g)(x)=f(g(x)) \\(fo\,g)(x)=f(\sqrt{x} )\\(fo\,g)(x)=2\,\sqrt{x}[/tex]
Base on this final expression, we understand that the Domain (numbers that can be used as input of the function and produce a real number as result) of this new function is limited to those x-values larger than or equal to zero. Negative numbers inside the square root will not produce a real number.
Therefore, the Domain is restricted to All Real numbers larger than or equal to o (zero).
This statement can also be given in inequality form as [tex]x\geq 0[/tex]
or in interval notation: [tex][0,\infty)[/tex]
