Question: a, b 5. Let fe C(V, W) and g E C(W, V). Suppose that there is some x e V, x / 0, with g(f

a, b

5. Let fe C(V, W) and g E C(W, V). Suppose that there is some x e V, x / 0, with g(f (x)) = x. Show that f (x) #0. (hint: Assume that f (x) =0, and find a contradiction.) b) Show that there is some y e W, y * 0, with f(g(y)) = y. (hint: Apply f to the first equation, and try and deduce a suitable y.)

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