Question

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

Answer 1

Answer:

All Real x larger or equal zero

or in inequality form: $x\geq 0$

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

Step-by-step explanation:

If $f(x)=2x$ and $g(x)=\sqrt{x}$, then using the definition for the composition of functions $(fo\,g)(x)=f(g(x))$, we get:

$(fo\,g)(x)=f(g(x)) \\(fo\,g)(x)=f(\sqrt{x} )\\(fo\,g)(x)=2\,\sqrt{x}$

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: $[0,\infty)$