Suppose that f is even and g is odd. a. Show that f o g is even. B. show that g o f is even .

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Suppose that f is even and g is odd. a. Show that f o g is even. B. show that g o f is even .

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Hey Conad :) If f(x) is an even function, it satisfies this property: f(-x) = f(x). If g(x) is an odd function, it satisfies this property: g(-x) = -g(x). So what happens when you take their composition. f(g(x)) = ? Well again, let's plug in the negative x and see what happens to the whole thing: =f(g(-x)) Since g is an odd function, g(-x) will become -g(x). =f(-g(x)) Since f is an even function, f(-stuff) will become f(stuff). =f(g(x)) So we just showed that f(g(-x)) = f(-g(x)) = f(g(x)). The same property that even functions have.

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