Thursday, August 28, 2008

Problem Of The Week 6



Let f(x) be as shown above. How many solutions does f(f(x))=6 have?

a) 2                b)  3                     c) 4                         d) 5                           e) 6

4 comments:

  1. My take (e)6
    f(x) should be 1 or -2 for f(f(x)) to be 6..Now draw a line y = 1 and y = -2, the lines touch the graph at 4+2 points

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  2. nicely done !!
    10/10

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  3. Cud u please post the detailed solution.. how to interpret the graph and construct one for f(f(x)).. its easier to do such problems graphically.. than the regular tedious way..

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  4. @vamsi,
    the solution given by bhaskar is pretty neat.
    Let me explain again

    f(f(x))=6 will have only two solutions in f(x) as shown in the graph that is f(x)=6 has two solutions in x
    hence f(x)=-2,1
    now we need to basically find the solutions of f(x)=-2,1 in x
    which can be done by drawing lines y=-2 and y=1 and letting them intersect the graph of y=f(x) we will get 6 points of intersection
    hence 6 solutions

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