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

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Re: If x ≠ 0, , let ♠ x be defined by the equation ♠x = x- 1/x. Then ♠(-3) [#permalink]
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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, ♠ $$-3 = (-3)-\frac{1}{-3}=(-3)-(-\frac{1}{3})=(-3)+ \frac{1}{3}=\frac{-9}{3}+ \frac{1}{3}= \frac{-8}{3}= -\frac{8}{3}$$

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Re: If x 0, , let x be defined by the equation x = x- 1/x. Then (-3) [#permalink]
Top Contributor
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)

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