I submitted this and the prof told me the results in one of my compositions is wrong.
(f ° g)(x) and (g ° f)(x)
f(x)=√(x+1),g(x)=x+2
f(x+2)=√(x+2+1)
=√(x+3)
=x+3
g(√(x+1))=√(x+1)+2
=x+1+2
=x+3

Question

I submitted this and the prof told me the results in one of my compositions is wrong.
(f ° g)(x)  and (g ° f)(x)
	f(x)=√(x+1),g(x)=x+2
	f(x+2)=√(x+2+1)
	                   =√(x+3)
	                   =x+3
	g(√(x+1))=√(x+1)+2
	                      =x+1+2
	                      =x+3

anonymous · Answer

f o g (x) = f ( sqrt (x+1) ) = sqrt [ sqrt (x+1) + 1 ]

anonymous · Answer

i messed up

anonymous · Answer

f o g (x) = f ( sqrt (x+1) ) = sqrt [ sqrt (x+1) + 1 ]

anonymous · Answer

correction f o g (x) = f ( x+2 ) = sqrt [ (x+2)+1) = sqrt ( x +  3)

anonymous · Answer

g o f ( x) = g ( sqrt (x+1) ) = sqrt (x+1) + 2

anonymous · Answer

you cant simplify that further