g(2x) =x^4 => g(2x)=16* g(x) -> option E

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:

Cheers,
Brent
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Given g(x)=\(X^4\)/16
g(2x)=\((2X)^4\)/16
g(2x)=\(2^4\)*\(X^4\)/16
g(2x)=16*g(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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g(2x) = (2x)^4/16 = 16x^4/16 = x^4

We see that g(2x) is 16 times g(x), i.e., g(2x) = 16g(x).

Answer: E
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