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

Question

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)

attari92 · Answer

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

BrentGMATPrepNow · Answer

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:  E

Cheers,
Brent

umadurga · Answer

Given g(x)= X^4 /16
g(2x)= (2X)^4 /16
g(2x)= 2^4 * X^4 /16
g(2x)=16*g(x)

ScottTargetTestPrep · Answer

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  = 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

ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

g(2x) = \frac{16x^4}{16}=x^4

g(x) = \frac{x^4}{16}

Thus, we have  16g(x) = 16\frac{x^4}{16}=x^4 , Answer must be (E)

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem ↧↧↧

https://www.youtube.com/watch?v=W4PtXbtYpvs

g(x) = \frac{x^4}{16}  and we need to find the value of  g(2x)  in terms of  g(x) ?

To find g(2x) we need to replace x with 2x in g(x)

=> g(2x) =  \frac{(2x)^4}{16}  =  \frac{2^4 * x^4}{16}  = 16 *  \frac{x^4}{16}  = 16* g(x)

So,  Answer will be E 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

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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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