If f(x)={(a+bx, x<1),(4 , x=1), (b-bx ,x>1)} & if lim x->1 f(x)=f(1) what are possible values of a & b? hence, find the value of f(-2)& f(2).

Asked by  | 2nd Mar, 2013, 10:20: PM

Expert Answer:

It seems like there is something wrong in the question, because the function doesn't seem to be continuous at x =1 because while the left hand limit at x = 1is a+b (Substituting x = 1 in a+bx), but the right hand limit at x = 1 is 0 (Substituting x =1 in b-bx) while the value of the function itself at x = 1 is 4. 
Furthermore, even if assume that everything is right and the function is discountinuous at x =1, and we assume that LHL = f(1), then we will get a+b = 4. Now, a and b can have all sorts of possible values, both integer and decimal values. So, its impossible to exactly define f(-2) and f(2) in that case again. 

Answered by  | 3rd Mar, 2013, 06:38: AM

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