SOLUTION: Let {{{f(x) = x^2-3x}}}. For what values of x is {{{f(f(x)) = f(x)}}}? Enter all the solutions, separated by commas.

Question 1156960: Let . For what values of x is ? Enter all the solutions, separated by commas.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!

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Values which should work are -1, 0, 3, 4.
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

The response from the other tutor makes solving the problem harder by multiplying polynomials when not necessary.

Treat the as a unit (a new "variable"):

Factor out one occurrence of the "variable" from each term:

Now solve by factoring each quadratic.

ANSWERS: x=0; x=3; x=4; x=-1

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