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anonymous
 one year ago
let f and g are functions that are neither even nor odd. a)Create an example where f+g is even, b) f+g is odd, c)f.g is even, d) f.g is odd
anonymous
 one year ago
let f and g are functions that are neither even nor odd. a)Create an example where f+g is even, b) f+g is odd, c)f.g is even, d) f.g is odd

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.1I give you one case , b, as example, you do the rest, ok? Let \(f(x) = x+3\) let check \(f(x) = x +3 \neq f(x) ~~hence,~~\text{f(x) is not even}\) \(f(x) = x3 \neq f(x)~~hence,~~\text{f(x) is not odd, therefore f(x) is neither even nor odd}\) Now, let \(g(x) = 2x3 \), let check \(g(x) = 2x3\neq g(x),~~hence,~~g(x) \text{is not even}\) \(g(x) = 2x+3 \neq g(x),~~hence~~\text{g(x) is not odd, hence g(x) is neither even nor odd}\) Now, combine \((f+g)(x) = f(x) +g(x) = x+32x3 = x\) let check \((f+g)(x) = x \\((f+g)(x) = (x) =x\) hence \((f+g)(x) = x=(f+g)(x)\), therefore \((f+g)(x) \)is an odd function.
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