composition functions - treatment 2

[logistic_guy]

here is the question

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

2. \(\displaystyle f(x) = x - 2, \ \ g(x) = \sqrt{x + 1}\)


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

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

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.

2. \(\displaystyle f(x) = x - 2, \ \ g(x) = \sqrt{x + 1}\)


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

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

is my analize correct?

Yes.

-Dan

 

[jonah2.0]

Beer induced reaction follows.

here is the question

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

2. \(\displaystyle f(x) = x - 2, \ \ g(x) = \sqrt{x + 1}\)


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

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

is my analize correct?

composition functions - treatment 2 logistic_guy

www.desmos.com

 

[logistic_guy]

Yes.

-Dan

thank topsquark very much

Beer induced reaction follows.

composition functions - treatment 2 logistic_guy

www.desmos.com

thank jonah very much
it's very easier to find the domain when i see the graph by my eye