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Algebra
21 Sep 2009 09:16:45 IST
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22 Sep 2009 08:43:12 IST
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| Can u pl xpalin? |
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24 Sep 2009 19:27:33 IST
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f(x) = -1, -2 ≤ x ≤ 0
= x -1, 0 < x ≤ 2
f(x) < 0 for -2 <=x<1, and f(x) >=0 for 1<=x<=2
Concept: |x| = x, if x >= 0
= -x if x < 0
Now..
g(x) = f( |x| ) + |f(x)|
Case 1: For x>=0, f(x)>=0. ( for 1<=x<=2 )
g(x) = f(x) + f(x) = 2(fx) = 2(x-1) = 2x - 2
Case 2: For x>=0, f(x) <0 ( for 0<=x<1 )
g(x) =f(x) - f(x) = 0
Case 3: For x<0, f(x)>=0 ( for NO value of x )
g(x) = f(-x) + f(x) CASE REJECTED
Case 4: For x<0, f(x)< 0 ( for -2<=x<=0 )
g(x) = f(-x) - f(x) = (-x-1) - (-1) = -x
Hence, g(x) = -x for -2<=x<0. g(x) = 0 for 0<=x<1 g(x) = 2x-2 for 1<=x<=2
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g(x) = -x for -2<= x <=0.
g(x) = 0 for 0< x <1
g(x) = 2x-2 for 1<= x <= 2
Pls rate if correct