How do you find the compositions given #f(x)=sqrt(x-3)#, #g(x)=sqrt(x +3)#?

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Answer 1 · 2017-05-18T23:29:04

#f(g(x)) = sqrt(sqrt(x + 3) - 3)#

#g(f(x)) = sqrt(sqrt(x - 3) + 3)#

The two possible compositions are #f(g(x))# and #g(f(x))#:

#Rightarrow f(g(x)) = f(sqrt(x + 3))#

#Rightarrow f(g(x)) = sqrt(sqrt(x + 3) - 3)#

#and#

#Rightarrow g(f(x)) = g(sqrt(x - 3))#

#Rightarrow g(f(x)) = sqrt(sqrt(x - 3) + 3)#