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Problem Of The Week 6

with 4 comments

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


Written by Implex

August 28, 2008 at 11:27 am

4 Responses

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  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

    Celebrating Life

    August 28, 2008 at 5:19 pm

  2. nicely done !!


    August 28, 2008 at 5:25 pm

  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..


    September 7, 2008 at 7:24 am

  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


    September 11, 2008 at 4:12 am

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