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If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3)

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Bunuel
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If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3) [#permalink] New post   07 Feb 2022, 08:15
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If \(x \neq 0\), let \(♠ x\) be defined by the equation \(♠x = x-\frac{1}{x}\). Then \(♠(-3) =\)

A. -10/3

B. -8/3

C. 0

D. 8/3

E. 10/3
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B
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B
JerryAtDreamScore
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If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3) [#permalink] New post   07 Feb 2022, 08:28
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Bunuel wrote:
If \(x \neq 0\), let \(♠ x\) be defined by the equation \(♠x = x-\frac{1}{x}\). Then \(♠(-3) =\)

A. -10/3

B. -8/3

C. 0

D. 8/3

E. 10/3


Replace all the x's with \(-3\). Then \(♠(-3) = (-3) - \frac{1}{(-3)} = -3 + \frac{1}{3} = -\frac{9}{3} + \frac{1}{3} = -\frac{8}{3}\)

Answer: B
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Re: If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3) [#permalink] New post   07 Feb 2022, 09:52
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Explanation:

\(♠ x\) be defined by the equation \(♠x = x-\frac{1}{x}\).

\(♠(-3) =\) \( -3 -\frac{1}{(-3)}\)
= -3 + (1/3)
= (-9+1) / 3
= -8/3

IMO-B
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Re: If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3) [#permalink] New post   07 Feb 2022, 09:59
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Bunuel wrote:
If \(x \neq 0\), let \(♠ x\) be defined by the equation \(♠x = x-\frac{1}{x}\). Then \(♠(-3) =\)

A. -10/3

B. -8/3

C. 0

D. 8/3

E. 10/3


Given: ♠ \(x = x-\frac{1}{x}\)
So, ♠ \(-3 = (-3)-\frac{1}{-3}=(-3)-(-\frac{1}{3})=(-3)+ \frac{1}{3}=\frac{-9}{3}+ \frac{1}{3}= \frac{-8}{3}= -\frac{8}{3}\)

Answer: B
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Re: If x 0, , let x be defined by the equation x = x- 1/x. Then (-3) [#permalink] New post   08 Aug 2022, 01:09
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Given that ♠ \(x = x-\frac{1}{x}\) and we need to find the value of ♠ (-3)

To find ♠ (-3) we need to compare what is after ♠ in ♠ (-3) and ♠ x

=> We need to substitute x with -3 in ♠ \(x = x-\frac{1}{x}\) to get the value of ♠ (-3)

=> ♠ \(-3 = -3 - \frac{1}{(-3)}\) = \( -3 + \frac{1}{3}\) = \(\frac{-9 + 1 }{3}\) = \(\frac{-8}{3}\)

So, Answer will be B
Hope it helps!

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Re: If x 0, , let x be defined by the equation x = x- 1/x. Then (-3) [#permalink]
08 Aug 2022, 01:09
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