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tifftifftiff5069
07.09.2020 •
Mathematics
Is it true that ƒ −(g − h) = (ƒ − g) − h? Explain why you believe the equation is true or provide a counterexample to show that it is not. A. Yes; the subtraction operation has the Commutative Property. B. Yes; the subtraction operation has the Associative Property. C. No; the subtraction operation does not have the Distributive Property. D. No; let ƒ(x) = x2, g(x) = x, and h(x) = 1. Then (ƒ − (g − h))(x) = x2 − x + 1 but ((ƒ − g) − h)(x) = x2 − x − 1.
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Ответ:
A
Step-by-step explanation:
Ok, in the first expression we have:
f - (g - h)
this can be written as:
f + (-1)*(g - h)
Now we can distribute that -1, because this is a scalar.
Now we have:
f + (-1)*g - (-1)*h
This is equal to:
f - g + h = (f - g) + h.
So the relation: ƒ −(g − h) = (ƒ − g) − h is wrong, and this is because the subtraction operation dos not have the distributive property. (when we "break" the parentheses, the sign of h should change)
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