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composite function (Posted on 2016-11-29) Difficulty: 2 of 5
It is given that f(x) = x^3 - 3x + 1 .

Find the number of real roots of f(f(x))

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution by graphing Comment 2 of 2 |
Plotting the composite function

(x^3 - 3x + 1)^3 - 3(x^3 - 3x + 1) + 1

on a grapher, we see 7 real roots.




The flatness at x=1 is probably related to the loss of 2 real roots (gaining two imaginary or composite roots) as there doesn't seem to be a discontinuity there, though it is indeed not your typical maximum.

  Posted by Charlie on 2016-11-29 13:59:19
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