Ultimate Quant Marathon Blog For IIM CAT

For All Your Quant Queries

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

Subscribe to comments with RSS.

  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 !!
    10/10

    outtimed

    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..

    Vamsi

    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

    outtimed

    September 11, 2008 at 4:12 am


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: