Question

For the given functions

Answer 1

put -x-1 into the x in f(x)

(1) (fog)(x) = f(g(x)) = f(-x-1) = -(-x-1)-1 = x+1-1 = x

(2) (gof)(x) = g(f(x)) = g(-x-1) = -(-x-1)-1 = x

(3) (fof)(x) = f(f(x)) = f(-x-1) = -(-x-1)-1 = x

(4) (gog)(x) = g(g(x)) = g(-x-1) = -(-x-1)-1 = x

So, for all the compositions, the result is x.

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