composition functions - treatment 3

[logistic_guy]

here is the question

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

3. $\displaystyle f(x) = \frac{1}{x}, \ \ g(x) = x^3 + 4$


my attemb
$\displaystyle f \circ g = f(g(x)) = \frac{1}{x^3 + 4}$
Domain: $\displaystyle x \neq \sqrt[3]{-4}$

$\displaystyle g \circ f = g(f(x)) = (\frac{1}{x})^3 + 4 = \frac{1}{x^3} + 4$
Domain: $\displaystyle x \neq 0$

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.

3. $\displaystyle f(x) = \frac{1}{x}, \ \ g(x) = x^3 + 4$


my attemb
$\displaystyle f \circ g = f(g(x)) = \frac{1}{x^3 + 4}$
Domain: $\displaystyle x \neq \sqrt[3]{-4}$

$\displaystyle g \circ f = g(f(x)) = (\frac{1}{x})^3 + 4 = \frac{1}{x^3} + 4$
Domain: $\displaystyle x \neq 0$

is my analize correct?

You tell us. Are there any x's that would make any of these expressions
$\dfrac{\text{something}}{0}$,

or
put a negative under a square root?

-Dan

 

[logistic_guy]

You tell us. Are there any x's that would make any of these expressions
$\dfrac{\text{something}}{0}$,

$\displaystyle x = 0$

put a negative under a square root?

we don't have square root

 

[topsquark]

$\displaystyle x = 0$


we don't have square root

I'm asking you to check your own work....

Those two are not the only criteria to worry about but they cover some 90% of what you will see.

-Dan

 

[logistic_guy]

I'm asking you to check your own work....

Those two are not the only criteria to worry about but they cover some 90% of what you will see.

-Dan

i'm not understand what you're trying to say
can you point out where my mistake?

 

[topsquark]

There is no mistake. These are elementary enough that I'm expecting you to check your own work now.

-Dan

 

[logistic_guy]

There is no mistake. These are elementary enough that I'm expecting you to check your own work now.

-Dan

i'm very happy i don't make mistake so far