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If \(\frac{1}{2}f(x) = f(\frac{x}{2})\), 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) \(f(x) =\sqrt{x-4}\)
31 Jul 2018, 01:45
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Bunuel
If \(\frac{1}{2}f(x) = f(\frac{x}{2})\), 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) \(f(x) =\sqrt{x-4}\)
the function should tell us that whenever we are adding any numeric value to x, say 10,2,1 etc, there will be no effect on f(x/2) but 1/2 f(x) will half it..
for example \(f(x) = 2x+2\) so \(\frac{1}{2} f(x) = \frac{(2x+2)}{2}=x+1\).......... BUT \(f(\frac{x}{2}) = \frac{2*x}{2}+2=x+2\)
therefore eliminate all those - A,D,E
whenever the equation is not linear, f(x/2) will change as the 2 in denominator will change by that power
for example \(f(x) = x^2...........\frac{1}{2}f(x)=\frac{x^2}{2}\) but \(f(\frac{x}{2})=\frac{x^2}{4}\)
eliminate C
if you understand teh above points, you will look for a linear x with no addition/subtraction of numeric value
such as 13x, 25x and so on
B
10 Aug 2018, 19:16
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Bunuel
If \(\frac{1}{2}f(x) = f(\frac{x}{2})\), 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 are given that ½f(x) = f(x/2). Let’s analyze the answer choices.
A) f(x) = 2x + 2
½f(x) = ½(2x + 2) = x + 1
f(x/2) = 2(x/2) + 2 = x + 2
We see that A is not true.
B) f(x/2) = 13x
½f(x) = ½(13x) = 13x/2
f(x/2) = 13(x/2) = 13x/2
We see that B is true.
Answer: B
