Question

If f(x) = 2x and g(x) = sqrt x,what is the domain of (fog)(x)?

Answer 1

A. x>0

Explanation:

E2021

Answer 2

All Real x larger or equal zero

or in inequality form:
`x\geq 0`

or in interval notation:
`[0,\infty)`

Explanation:

If
`f(x)=2x` and
`g(x)=√(x)`, then using the definition for the composition of functions
`(fo\,g)(x)=f(g(x))`, we get:

`(fo\,g)(x)=f(g(x)) \\(fo\,g)(x)=f(√(x) )\\(fo\,g)(x)=2\,√(x)`

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
`x\geq 0`

or in interval notation:
`[0,\infty)`