Composition of functions

• Jan 8th 2010, 10:15 PM
redcherry
Composition 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 PM
mr fantastic
Quote:

Originally Posted by redcherry
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)

What have you tried and where are you stuck?
• Jan 8th 2010, 10:35 PM
redcherry
tq~
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 AM
HallsofIvy
Quote:

Originally Posted by redcherry
f(g(x))=f((x^2+3)^(1/2))
=((x^2+3)^(1/2)-3)^(1/2))

i stuck at here..

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.