find the composition of f with g and state the domain..

f(x)=(x-3)^(1/2), g(x)=(x^2+3)^(1/2)

tenQ(Wink)

Printable View

- Jan 8th 2010, 10:15 PMredcherryComposition of functions
find the composition of f with g and state the domain..

f(x)=(x-3)^(1/2), g(x)=(x^2+3)^(1/2)

tenQ(Wink) - Jan 8th 2010, 10:15 PMmr fantastic
- Jan 8th 2010, 10:35 PMredcherrytq~
f(g(x))=f((x^2+3)^(1/2))

=((x^2+3)^(1/2)-3)^(1/2))

i stuck at here.. - Jan 9th 2010, 04:36 AMHallsofIvy
Okay, you've found the composition so the only thing left to do is state the domain! The only "problem" appears to be square roots. Obviously $\displaystyle x^2+ 3$ is never negative so your only condition is that you must have $\displaystyle (x^2+3)^{1/2}\ge 3$. What values of x satisfy that?

The**equation**$\displaystyle (x^2+3)^{1/2}= 3$ gives values of x that separate "<" from ">". Find those and determine which of the intervals separated by those values satisfy the inequality.