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If g is a function defined for all x by g(x) = x^4/16, then what is

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If g is a function defined for all x by g(x) = x^4/16, then what is [#permalink]

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New post 03 May 2017, 03:26
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If g is a function defined for all x by \(g(x) = \frac{x^4}{16}\), then what is the value of \(g(2x)\) in terms of \(g(x)\)?

(A) \(\frac{g(x)}{16}\)

(B) \(\frac{g(x)}{4}\)

(C) \(4g(x)\)

(D) \(8g(x)\)

(E) \(16g(x)\)
[Reveal] Spoiler: OA

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Re: If g is a function defined for all x by g(x) = x^4/16, then what is [#permalink]

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New post 03 May 2017, 03:32
g(2x) =x^4 => g(2x)=16* g(x) -> option E
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Re: If g is a function defined for all x by g(x) = x^4/16, then what is [#permalink]

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New post 03 May 2017, 04:48
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Bunuel wrote:
If g is a function defined for all x by \(g(x) = \frac{x^4}{16}\), then what is the value of \(g(2x)\) in terms of \(g(x)\)?

(A) \(\frac{g(x)}{16}\)

(B) \(\frac{g(x)}{4}\)

(C) \(4g(x)\)

(D) \(8g(x)\)

(E) \(16g(x)\)


One option is to PLUG IN a value for x, and see what we get.

Let's try x = 1

So, g(x) = g(1) = (1^4)/16 = 1/16

Now let's try g(2x). If x = 1, then 2x = (2)(1) = 2
So, g(2x) = g(2) = (2^4)/16 = 16/16 = 1

So, when x = 1, g(x) = 1/16, and g(2x) = 1
In other words, the value of g(2x) is 16 TIMES the value of g(x)

Answer:
[Reveal] Spoiler:
E


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Brent
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Re: If g is a function defined for all x by g(x) = x^4/16, then what is [#permalink]

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New post 03 May 2017, 06:16
Given g(x)=\(X^4\)/16
g(2x)=\((2X)^4\)/16
g(2x)=\(2^4\)*\(X^4\)/16
g(2x)=16*g(x)
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Re: If g is a function defined for all x by g(x) = x^4/16, then what is [#permalink]

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New post 06 May 2017, 16:31
Bunuel wrote:
If g is a function defined for all x by \(g(x) = \frac{x^4}{16}\), then what is the value of \(g(2x)\) in terms of \(g(x)\)?

(A) \(\frac{g(x)}{16}\)

(B) \(\frac{g(x)}{4}\)

(C) \(4g(x)\)

(D) \(8g(x)\)

(E) \(16g(x)\)


Let’s begin by calculating g(2x):

g(2x) = (2x)^4/16 = (16x^4)/16 = x^4

Now, since g(x) = (x^4)/16, we have:

g(2x) = x^4 = (16x^4)/16 = 16[(x^4/16)] = 16g(x)

Alternate Solution:

When x = 1, g(2x) = g(2) = (2^4)/16 = 1. We will test each answer choice to see which ones produce 1 when x = 1. Note that g(1) = 1^4/16 = 1/16.

Answer Choice A: g(x)/16

When x = 1, we have g(1)/16 = (1/16)/16 = 1/16^2 ≠ 1.

Answer Choice B: g(x)/4

When x = 1, we have g(1)/4 = (1/16)/4 = 1/64 ≠ 1.

Answer Choice C: 4g(x)

When x = 1, we have 4g(x) = 4(1/16) = 4/16 = 1/4 ≠ 1.

Answer Choice D: 8g(x)

When x = 1, we have 8g(x) = 8(1/16) = 8/16 = 1/2 ≠ 1.

Answer Choice E: 16g(x)

When x = 1, we have 16g(x) = 16(1/16) = 16/16 = 1.

Answer: E
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Re: If g is a function defined for all x by g(x) = x^4/16, then what is   [#permalink] 06 May 2017, 16:31
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