We are given that f(x)=sqrt(x) and g(x) = x+1:

We are asked to find the composition of the functions:

(1) fog(x)=f(g(x)) We substitute the expression for g(x) for x in f(x).

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

(2) gof(x)=g(f(x)) We substitute the expression for f(x) into g(x):

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

Note that f(g(x)) is not equal to g(f(x)). f(g(x)) is the square root function shifted left one unit, while g(f(x)) is the square root function shifted up 1 unit.

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