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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value

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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value  [#permalink]

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31 May 2018, 10:59
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Given $$\frac{1}{2} f(x)= f(\frac{1}{2}*x)$$, which of the following is true for all values of f(x)?

A. $$f(x)= 2x+2$$

B. $$f(x)=13x$$

C. $$f(x)=x^2$$

D. $$f(x)=x-10$$

E. $$f(x)=\sqrt{(x-4)}$$

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Given 1/2*f(x)= f(1/2*x), which of the following is true for all value  [#permalink]

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31 May 2018, 23:12
Calculating $$\frac{1}{2} * f(x)$$ for each of the answer options, we get
A. $$f(x)= 2x+2$$ -> $$\frac{1}{2} * f(x) = \frac{2(x+1)}{2} = (x+1)$$. Now, $$f(\frac{1}{2}*x) = 2*\frac{1}{2}*x + 2 = x + 2$$

B. $$f(x)=13x$$ -> $$\frac{1}{2} * f(x) = \frac{13x}{2}$$. Now, $$f(\frac{1}{2}*x) = 13*\frac{x}{2}= \frac{13x}{2}$$

We have a match for $$\frac{1}{2} * f(x) = f(\frac{1}{2}*x)$$

Therefore, Option B [f(x) = 13x] is the correct answer.
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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value  [#permalink]

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03 Jun 2018, 17:28
Bunuel wrote:
Given $$\frac{1}{2} f(x)= f(\frac{1}{2}*x)$$, which of the following is true for all values of f(x)?

A. $$f(x)= 2x+2$$

B. $$f(x)=13x$$

C. $$f(x)=x^2$$

D. $$f(x)=x-10$$

E. $$f(x)=\sqrt{(x-4)}$$

We can let x = 2, and we have:

½f(2) = f(1)

A) f(x) = 2x + 2

½f(2) = ½(2(2) + 2) = ½(6) = 3

f(1) = 2(1) + 2 = 4

A is not correct.

B) f(x) = 13x

½f(2) = ½(13(2)) = ½(26) = 13

f(1) = 13(1) = 13

B is correct.

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Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value  [#permalink]

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04 Jun 2018, 01:38
1
Bunuel wrote:
Given $$\frac{1}{2} f(x)= f(\frac{1}{2}*x)$$, which of the following is true for all values of f(x)?

A. $$f(x)= 2x+2$$

B. $$f(x)=13x$$

C. $$f(x)=x^2$$

D. $$f(x)=x-10$$

E. $$f(x)=\sqrt{(x-4)}$$

Re-writing the given function as f(x)=2f($$\frac{x}{2}$$)

Let's check the validity of the given answer choices.

A. 2f($$\frac{x}{2}$$)=2(($$\frac{x}{2}$$)+2)=$${x+4}\neq{f(x)}$$
B. 2f($$\frac{x}{2}$$)=$$2(13*\frac{x}{2})$$=13x=f(x)

hence option(B) is the correct answer.
Re: Given 1/2*f(x)= f(1/2*x), which of the following is true for all value &nbs [#permalink] 04 Jun 2018, 01:38
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