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Function F(x) is defined as follows: if x is positive or 0 then F(x) = 1 - x; if x is negative then F(x) = x - 1.
Which of the following is true about F(x)?
I. F(|x|) = |F(x)| II. F(x) = F(-x) III. |F(x + 1)| = |x|
I. F(|x|) = |F(x)| :- not possible.
First, F(|x|) could be -ve, 0 and +ve but |F(x)| is always 0 or +ve.
If |x| is greater than 1, F(|x|) = 1 - lxl is -ve fraction or > 1. If |x| is smaller than 1, F(|x|) = 1 - |x| is +ve fraction. If |x| is 0, F(|x|) is 1.
But |F(x)| is always 0 or +ve. So not true.
II. F(x) = F(-x):- not possible. If x is +ve, -x is -ve and vice versa.
If x is 0, F(x) = F(-x) = 1 If x is +ve, F(x) = 1 - x, which could be +ve if x is smaller than 1 or -ve if x is > 1, and F(-x) = -x-1, which could also be -ve if x is >-1 or +ve if x is <-1. Similarly, if x is negative, then F(x) and F(-x) will have +ve or -ve values.
They are not equal. not suff.
III. |F(x + 1)| = |x|:- is possible.
|F(x + 1)| is always |x| whether (x+1) is +ve or -ve.
If (x + 1) is +ve, |F(x + 1)| = |1- (x + 1)| = |x| If (x + 1) is -ve, |F(x + 1)| = |(x + 1)-1| = |x|
GMAT TIGER's explanation is right but you are not supposed to write Math major test. Just take x=2 and x=-2. Then apply on the rule. Its time consuming not tough. In fact it is easy. It took 2 min for me to solve this one.
It will take 5-6 min to draw a graph for most of the guys.
just by looking at the functions you can tell that 1 & 2 are not valid because they are saying that the value of X is the same, before and after the function which we know is untrue as depending on the value of X it will either be subtracted from 1 or 1 will be added to it.
for answer 3, if you subtract 1 and then add 1 back, you will have your original number in absolute terms. if you subtract your original number from 1 and then add 1 back, you will have your number in absolute terms. therefore answer is C.
It seems as if it's time consuming and then you begin to panic and want to guess so you can do it in under 2 minutes, but if you do as silasaaa2 suggests and just substitute. Pick a positive and negative number and substitute for each. You WILL find the answer in less than 2 minutes.
30 seconds to substitute and confirm C. Do not solve these type of questions unless of course this is your 37th question and you have 15 mns spare time. Even then, I would prefer not to solve, but substitute for this question