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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
Posted in Functions, Problem of the week
Tagged with Functions, Problem of the week
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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
August 28, 2008 at 5:19 pm
nicely done !!
August 28, 2008 at 5:25 pm
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
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
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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