PhiBeeandJay
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Find f(-x)-f(x) for the following function:
f(x)=x^3+x-9
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Mertsj
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What is f(-x)?
PhiBeeandJay
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The question didn't say and so I'm stuck.
anonymous
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\(f(3)=3^2+3-9=27+3-9=21\)
\(f(-3)=(-3)^2+(-3)-9=-27-3-9=-39\)
\(-39-21=-60\)
now try it with just \(x\) and \(-x\)
anonymous
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\(f(-x)\) is confusing, but it means replace \(x\) everywhere by \(-x\)
anonymous
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so first step is to write \(f(-x)= (-x)^3+(-x)-9\) and then simplify a big
take that answer, and subtract \(x^3+x-9\) from it
make sure to use parentheses
PhiBeeandJay
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So it would be -x-x-9-(x^2+x-9)?
anonymous
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i assume you mean
\[-x^3-x-9-(x^3+x-9)\]
PhiBeeandJay
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Yes.
anonymous
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ok good, now remove the parentheses by distributing the minus sign, then combine like terms
PhiBeeandJay
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Thank you!
anonymous
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yw hope it is clear