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Which of the following functions, f defined for all numbers x, has the

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Which of the following functions, f defined for all numbers x, has the [#permalink] New post   05 Sep 2023, 06:55
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Which of the following functions, f defined for all numbers x, has the property that\( f(–x) = –ƒ(x)\) for all numbers x?


A. \(f(x) = |x| – x\)

B. \(f(x) = x(x^4– x)\)

C. \(f(x) = x – x^3
\)

D.\( f(x) =\frac{ x^2}{x^2+1}\)

E. \(f(x) = ( x^3 + x)^4\)
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Re: Which of the following functions, f defined for all numbers x, has the [#permalink] New post   08 Sep 2023, 11:55
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f(-x) = - f(x)
Substitute -x into the functions.
A. |-x| - x = x - x = 0 ; does not equal - |x| + x
B. (-x)((-x)^4 -(-x)) = (-x)(x^4 + x); does not equal -x(x^4-x)
C. (-x) - (-x)^3 = -x + x^3 = - (x-x^3); equals - (x-x^3)

C is the correct answer.
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Re: Which of the following functions, f defined for all numbers x, has the [#permalink]
08 Sep 2023, 11:55
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