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# For which of the following functions f(x) = f(-x)?

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Senior Manager
Joined: 17 Oct 2016
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For which of the following functions f(x) = f(-x)?  [#permalink]

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08 Mar 2019, 23:19
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Difficulty:

25% (medium)

Question Stats:

66% (01:14) correct 34% (01:04) wrong based on 32 sessions

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For which of the following functions f(x) = f(-x)?

A. f(x) =$$x^3$$ +3x

B. f(x) = $$x^3$$

C. f(x) = $$x^2$$ - 2x

D. f(x) = $$(x-3)^2$$

E. f(x) = (x+2)(x-2)

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Re: For which of the following functions f(x) = f(-x)?  [#permalink]

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09 Mar 2019, 07:50
fitzpratik wrote:
For which of the following functions f(x) = f(-x)?

A. f(x) =$$x^3$$ +3x

B. f(x) = $$x^3$$

C. f(x) = $$x^2$$ - 2x

D. f(x) = $$(x-3)^2$$

E. f(x) = (x+2)(x-2)

A. f(x) =$$x^3$$ +3x
f(-x) =-$$x^3$$ -3x = -f(x)
Hence not equal f(x)

B. f(x) = $$x^3$$
f(-x) = -$$x^3$$ = -f(x)
Hence not equal f(x)

C. f(x) = $$x^2$$ - 2x
f(-x) = $$x^2$$ + 2x
Hence not equal f(x)

D. f(x) = $$(x-3)^2$$
f(-x) = $$(-x-3)^2$$
Hence not equal f(x)

E. f(x) = (x+2)(x-2)
f(-x) = (-x+2)(-x-2) = -(2-x)(x+2) = (x+2)(x-2) = f(x)

Hence E is the correct answer.
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Re: For which of the following functions f(x) = f(-x)?   [#permalink] 09 Mar 2019, 07:50
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