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What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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31 Oct 2012, 00:57
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Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A. x  10 B. 3x + 10 C. x D. x  5 E. x What is wrong with Thanks & Regards Vinni
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Last edited by Bunuel on 31 Oct 2012, 04:04, edited 1 time in total.
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vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A). x  10 B). 3x + 10 C). x D). x  5 E). x What is wrong with Thanks & Regards Vinni From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps..
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Vips0000 wrote: From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. Well, I haven't understood completely. All i know from my knowledge that a  b = b  a So, as you have explained above x5 x5 = 0 Now we are left with x According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. 5 = 5. This is the exact reason i selected E as the answer. I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement " It can not be E because x <> x for any negative value of x." Thanks & Regards Vinni



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31 Oct 2012, 21:31
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vinnik wrote: Vips0000 wrote: From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. Well, I haven't understood completely. All i know from my knowledge that a  b = b  a So, as you have explained above x5 x5 = 0 Now we are left with x According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. 5 = 5. This is the exact reason i selected E as the answer. I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement " It can not be E because x <> x for any negative value of x." Thanks & Regards Vinni Two points that you are confused with: x = x This is exactly same thing as you have mentioned: "All i know from my knowledge that a  b = b  a" Now second point, x <> x for any negative number x. Well, take for example x =5 in this case, x= 5 and x=5 Are these 5 and 5 equal? no. That is x <> x for any negative number x. What you are confusing this is with x=x Hope it is clear.
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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20 Nov 2012, 10:23
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vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A. x  10 B. 3x + 10 C. x D. x  5 E. x What is wrong with Thanks & Regards Vinni how i solved this ques: f(x)  g(x) = 0. Because, f(x) and g(x) both represents distance between x & 5. Therefore, we have to solve only this f(g(x) => f(5x)= 5x5 = x
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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21 Nov 2012, 21:32
greatps24 wrote: vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A. x  10 B. 3x + 10 C. x D. x  5 E. x What is wrong with Thanks & Regards Vinni how i solved this ques: f(x)  g(x) = 0. Because, f(x) and g(x) both represents distance between x & 5. Therefore, we have to solve only this f(g(x) => f(5x)= 5x5 = x I am confused as in the value of x will always be x so why are we choosing x ?
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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22 Nov 2012, 06:01
Kudos Bunuel. Thanks for clarifying One point: what if in answer choices we also have x (and x)?
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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05 Dec 2012, 21:58
Bunuel wrote: greatps24 wrote: Kudos Bunuel. Thanks for clarifying
One point: what if in answer choices we also have x (and x)? x and x are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices? Kudos Bunuel. Cheers
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Re: function [#permalink]
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09 Feb 2013, 04:08
Vips0000 wrote: vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A). x  10 B). 3x + 10 C). x D). x  5 E). x What is wrong with Thanks & Regards Vinni From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. Got a doubt... f(g(x) = f(5x) = 5x5 =x Why (5x) is considered without Mod sign. Ideally it should have been f(5x) = (5x)5 If we simplify this we get two options x10 and x. Why this is not correct ??



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Re: function [#permalink]
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09 Feb 2013, 04:19
mani6389 wrote: Vips0000 wrote: vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A). x  10 B). 3x + 10 C). x D). x  5 E). x What is wrong with Thanks & Regards Vinni From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. Got a doubt... f(g(x) = f(5x) = 5x5 =x Why (5x) is considered without Mod sign. Ideally it should have been f(5x) = (5x)5 If we simplify this we get two options x10 and x. Why this is not correct ?? f(g(x)) has only one modulus. g(x)=5x, thus f(g(x)) = f(5x). Next, since f(5x) = 5x5=x, then f(5x) = x = x. Hope it's clear.
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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22 Feb 2013, 22:27
Let f(a) = a  5 g(b) = 5  b.
What is the value of f(x)  g(x) + f(g(x) ?
A. x  10 B. 3x + 10 C. x D. x  5 E. x
hi in the above question it is asking the value of the equation f(x)  g(x) + f(g(x)....
when we put in the values appropriately:
x55x+5x5 =x
mod of x=x
i understand the piece tht
when we have the value as x and we take modulous then it gives the values as positive values of x.
x is not equal to x
but here it is asking us the eventual result of the equation so when we get x we get the final result, it is positive values of x.



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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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24 Feb 2013, 08:23
x is the answer.
x not necessarily is equal to x , as it would depend upon the whether x is +ve or ve.



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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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24 Feb 2013, 21:20
mehasingh wrote: Let f(a) = a  5 g(b) = 5  b.
What is the value of f(x)  g(x) + f(g(x) ?
A. x  10 B. 3x + 10 C. x D. x  5 E. x
hi in the above question it is asking the value of the equation f(x)  g(x) + f(g(x)....
when we put in the values appropriately:
x55x+5x5 =x
mod of x=x
i understand the piece tht
when we have the value as x and we take modulous then it gives the values as positive values of x.
x is not equal to x
but here it is asking us the eventual result of the equation so when we get x we get the final result, it is positive values of x. You are assuming that x is positive. x = x in any case. x may be positive or negative. Take examples: Say x = 5, 5 = 5 = 5 Say x = 5, (5) = 5 = 5 Hence (C) is correct. But to remove the mod, you must know the sign of x. By definition, x = x when x is positive x = x when x is negative x = x = x only when x is positive If x is negative, say x = 1, x = (1) = 1 which is not the same as x. Hence \(x \neq x\) when x is negative. Since we have no information on the sign of x, we cannot say that x = x.
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Re: function [#permalink]
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16 Mar 2013, 21:16
Vips0000 wrote: vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A). x  10 B). 3x + 10 C). x D). x  5 E). x What is wrong with Thanks & Regards Vinni From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\) Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. Can any1 explain why \(= x5 5x+x\) \(=x5 x5+x\) 5x = x5 ??? Thank you



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22 May 2013, 02:37
Vips0000 wrote: vinnik wrote: Let f(a) = a  5 g(b) = 5  b. What is the value of f(x)  g(x) + f(g(x) ? A). x  10 B). 3x + 10 C). x D). x  5 E). x What is wrong with Thanks & Regards Vinni From question: \(f(x) = x5\) \(g(x) =5x\) \(f(g(x) = f(5x) = 5x5 =x\)Now: \(f(x)  g(x) + f(g(x)\) \(= x5 5x+x\) \(=x5 x5+x\) \(=x\) Ans C. It can not be E because x <> x for any negative value of x. Hope it helps.. How did you get that part I didn't understand that I understood the rest why is it 5x5?
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Re: What is the value of f(x)  g(x) + f(g(x) ? [#permalink]
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22 May 2013, 06:56
one more question if we were given X is positive or negative then the answer would be E?
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