Final answer:
To show that if f∘g is one-to-one, then g must also be one-to-one, we need to prove that if g(a) = g(b), then a = b. Therefore, if f∘g is one-to-one, then g must also be one-to-one.
Step-by-step explanation:
To show that if f∎g is one-to-one, g must also be one-to-one, we need to prove that if g(a) = g(b), then a = b. Since we know that f∎g is one-to-one, it means that if f(g(a)) = f(g(b)), then g(a) = g(b) and a = b.
Let's assume that g(a) = g(b). Then, we have:
f(g(a)) = f(g(b)) (since f∎g is one-to-one)
a = b (since we know that if f(g(a)) = f(g(b)), then g(a) = g(b) and a = b)
Therefore, if f∎g is one-to-one, then g must also be one-to-one.