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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:28) correct
37%
(01:45)
wrong
based on 208
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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. \(f(x)=\sqrt{(x-4)}\)
A. \(f(x)= 2x+2\)
B. \(f(x)=13x\)
C. \(f(x)=x^2\)
D. \(f(x)=x-10\)
E. \(f(x)=\sqrt{(x-4)}\)
01 Jun 2018, 00:12
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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.
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.
03 Jun 2018, 18:28
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Bunuel
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. \(f(x)=\sqrt{(x-4)}\)
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)
Let’s analyze each answer choice:
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.
Answer: B
