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If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3)
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Bunuel
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If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink] New post  26 Nov 2020, 06:09
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If \(g\) is the function defined by \(g(x)=\frac{(6x-3)(x+4)}{(x-1)(x+2)(x-3)}\) then \(g(x)\) is is undefined for which of the following values of x?

I. 1
II. -2
III. 3

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
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sahuayush
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Re: If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink] New post  26 Nov 2020, 06:37
E

Reason:

By substituting each of these values one by one, the denominator becomes 0, thus undefined.

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EgmatQuantExpert
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Re: If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink] New post  27 Nov 2020, 23:38
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Solution



Given
In this question, we are given that
    • A function g, which is defined by \(g(x)=\frac{(6x-3)(x+4)}{(x-1)(x+2)(x-3)}\)

To find
We need to determine
    • The values of x, for which g(x) is undefined

Approach and Working out
As g(x) is in the form A/B, the function g(x) will be undefined when the denominator B will become 0.
Here, the denominator is in the form of a product of three elements: (x – 1), (x + 2), and (x – 3)
If the product of these elements is 0, then at least one of these 3 elements must be equal to 0
    • If (x – 1) = 0, then x = 1
    • If (x + 2) = 0, then x = -2
    • If (x – 3) = 0, then x = 3
Hence, x can be either 1 or -2 or 3.

Thus, option E is the correct answer.

Correct Answer: Option E
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Re: If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink] New post  27 Nov 2020, 23:51
Asked: If \(g\) is the function defined by \(g(x)=\frac{(6x-3)(x+4)}{(x-1)(x+2)(x-3)}\) then \(g(x)\) is is undefined for which of the following values of x?

I. 1
II. -2
III. 3

For 1, -2 & 3, denominator becomes 0 and function become undefined.

IMO E
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Re: If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink] New post  23 Apr 2022, 00:52
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Re: If g is the function defined by g(x) = (6x - 3)(x + 4)/(x-1)(x+2)(x-3) [#permalink]
23 Apr 2022, 00:52
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