composition functions - treatment 5

[logistic_guy]

here is the question

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

5. \(\displaystyle f(x) = x^2 + 1, \ \ g(x) = \sin x\)


my attemb
\(\displaystyle f \circ g = f(g(x)) =\sin^2 x + 1\)
Domain: \(\displaystyle (-\infty,\infty)\)

\(\displaystyle g \circ f = g(f(x)) = \sin(x^2 + 1)\)
Domain: \(\displaystyle (-\infty,\infty)\)

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.

5. \(\displaystyle f(x) = x^2 + 1, \ \ g(x) = \sin x\)


my attemb
\(\displaystyle f \circ g = f(g(x)) =\sin^2 x + 1\)
Domain: \(\displaystyle (-\infty,\infty)\)

\(\displaystyle g \circ f = g(f(x)) = \sin(x^2 + 1)\)
Domain: \(\displaystyle (-\infty,\infty)\)

is my analize correct?

Did you graph these?

-Dan

 

[logistic_guy]

Did you graph these?

-Dan

that's for \(\displaystyle f \circ g\)



that's for \(\displaystyle g \circ f\)

 

[khansaheb]

that's for \(\displaystyle f \circ g\)

View attachment 38974

that's for \(\displaystyle g \circ f\)

View attachment 38975

So from the graphs - what do you conclude about the domain of f o g or g o f ?

 

[logistic_guy]

So from the graphs - what do you conclude about the domain of f o g or g o f ?

infinite domain

 

[khansaheb]

infinite domain

Do you expect any discontinuity in fog or gof ?

 

[logistic_guy]

Do you expect any discontinuity in fog or gof ?

no never

 

[khansaheb]

here is the question

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

5. \(\displaystyle f(x) = x^2 + 1, \ \ g(x) = \sin x\)


my attemb
\(\displaystyle f \circ g = f(g(x)) =\sin^2 x + 1\)
Domain: \(\displaystyle (-\infty,\infty)\)

\(\displaystyle g \circ f = g(f(x)) = \sin(x^2 + 1)\)
Domain: \(\displaystyle (-\infty,\infty)\)

is my analize correct?

Then your analysis is correct.

 

[logistic_guy]

Then your analysis is correct.

thank khan very much

i feel i'm progressing very quickly in the field of domain