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

Expert replies
by AAPL » Fri Apr 27, 2018 5:21 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty

If g is a function defined for all x by g(x) = (x^4)/16, then what is the value of g(2x) in terms of g(x)?

$$A.\ \frac{g\left(x\right)}{16}$$
$$B.\ \frac{g\left(x\right)}{4}$$
$$C.\ 4g\left(x\right)$$
$$D.\ 8g\left(x\right)$$
$$E.\ 16g\left(x\right)$$

The OA is E.

I solved this PS question as follows,

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

Option E.

Has anyone another approach to solve this PS question? Regards!
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Source: — Problem Solving |

by GMATGuruNY » Fri Apr 27, 2018 5:36 am
AAPL wrote:If g is a function defined for all x by g(x) = (x^4)/16, then what is the value of g(2x) in terms of g(x)?

$$A.\ \frac{g\left(x\right)}{16}$$
$$B.\ \frac{g\left(x\right)}{4}$$
$$C.\ 4g\left(x\right)$$
$$D.\ 8g\left(x\right)$$
$$E.\ 16g\left(x\right)$$
Let x=2, with the result that g(x) = g(2) = 2�/16 = 1.
The question stem asks for the value of g(2x):
g(2x) = g(2*2) = g(4) = 4�/16 = (16*16)/16 = 16.
Now plug g(x) = 1 into the answers to see which yields the target value of 16 for g(2x).
Only E works:
16g(x) = 16*1 = 16.

The correct answer is E.
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by Vincen » Fri Apr 27, 2018 7:12 am
Hi AAPL.

For me, the best way is the way you did it. Another way (almost the same) is:

$$g\left(x\right)=\frac{x^4}{16}=\left(\frac{x}{2}\right)^4.$$ Then $$g\left(2x\right)=\left(\frac{2x}{2}\right)^4=x^4=16\left(\frac{x^4}{16}\right)=16\cdot g\left(x\right).$$ The corretc answer is E.

I hope it helps you.
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by Scott@TargetTestPrep » Mon Apr 30, 2018 3:43 pm
AAPL wrote:If g is a function defined for all x by g(x) = (x^4)/16, then what is the value of g(2x) in terms of g(x)?

$$A.\ \frac{g\left(x\right)}{16}$$
$$B.\ \frac{g\left(x\right)}{4}$$
$$C.\ 4g\left(x\right)$$
$$D.\ 8g\left(x\right)$$
$$E.\ 16g\left(x\right)$$
We see that g(2x) = (2x)^4/16 = 16x^4/16 = x^4.

Since g(x) = x^4/16 and g(2x) = x^4, we have:

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

16 * g(x) = g(2x)

Answer: E

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