composition functions - treatment 1

[logistic_guy]

here is the question

Find the compositions $\displaystyle f \circ g$ and $\displaystyle g \circ f$, and identify their respective domains.

1. $\displaystyle f(x) = x + 1, \ \ g(x) = \sqrt{x - 3}$


my attemb
recently i take rigorous treatment in algebra and i master $\displaystyle 99\%$
some fragments remain unmastered, particulary the domain of composition function
most of the time, i get the domain wrong
so i'll make $\displaystyle 6$ treatments to hope finally i overcome this tiny issue

$\displaystyle f \circ g = f(g(x)) = \sqrt{x - 3} + 1$
Domain: $\displaystyle x \geq 3$

$\displaystyle g \circ f = g(f(x)) = \sqrt{x + 1 - 3} = \sqrt{x - 2}$
Domain: $\displaystyle x \geq 2$

is my analize correct?

 

[topsquark]

here is the question

Find the compositions $\displaystyle f \circ g$ and $\displaystyle g \circ f$, and identify their respective domains.

1. $\displaystyle f(x) = x + 1, \ \ g(x) = \sqrt{x - 3}$


my attemb
recently i take rigorous treatment in algebra and i master $\displaystyle 99\%$
some fragments remain unmastered, particulary the domain of composition function
most of the time, i get the domain wrong
so i'll make $\displaystyle 6$ treatments to hope finally i overcome this tiny issue

$\displaystyle f \circ g = f(g(x)) = \sqrt{x - 3} + 1$
Domain: $\displaystyle x \geq 3$

$\displaystyle g \circ f = g(f(x)) = \sqrt{x + 1 - 3} = \sqrt{x - 2}$
Domain: $\displaystyle x \geq 2$

is my analize correct?

Yes.

-Dan

 

[logistic_guy]

Yes.

-Dan

thank topsquark very much