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anonymous
 one year ago
In 1A4 B, we are trying to show that an even polynomial = even + odd functions. However the starting function on the problem sheet is different than the starting one on the answer sheet. Is this a mistake or an extra step?
anonymous
 one year ago
In 1A4 B, we are trying to show that an even polynomial = even + odd functions. However the starting function on the problem sheet is different than the starting one on the answer sheet. Is this a mistake or an extra step?

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phi
 one year ago
Best ResponseYou've already chosen the best response.1The equation for f(x) in 1A4 (b) has a typo. They wanted to write an identity, which we can derive. Begin by writing f(x) this way: \[ f(x)= \frac{f(x)}{2} + \frac{f(x)}{2} \] and then add and subtract f(x)/2 (which adds zero): \[ f(x)= \frac{f(x)}{2} + \frac{f(x)}{2} + \frac{f(x)}{2}  \frac{f(x)}{2} \] and reorder the terms to get \[ f(x)= \frac{f(x)}{2} + \frac{f(x)}{2}+ \frac{f(x)}{2}  \frac{f(x)}{2} \\ f(x)= \frac{f(x)+f(x)}{2} + \frac{f(x)f(x)}{2} \] if we simplify the righthand side we get f(x), so the identity is clearly true. But as the answer shows, the two terms represent even and odd functions that add up to create f(x)
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