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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 |x-5|- |x-5| = 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."

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 |x-5|- |x-5| = 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.

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?
_________________

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x| Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5| If we simplify this we get two options |x-10| and |x|. Why this is not correct ??

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x| Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5| If we simplify this we get two options |x-10| and |x|. Why this is not correct ??

|f(g(x))| has only one modulus.

g(x)=5-x, thus |f(g(x))| = |f(5-x)|.

Next, since f(5-x) = 5-x-5=-x, then |f(5-x)| = |-x| = |x|.