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

Answer 1

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

Answer 2

i messed up

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

you cant simplify that further