If f(x) = f(3x - 1), for f(x) = x² - 4x + 11 find x.
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Combining the given information we have
x^2–4x+11 = (3x-1)^2–4(3x-1)+11
<=>
x^2–4x = [9x^2–6x+1]-12x+4 = 9x^2 -18x + 5
<=>
0 = 8x^2 -14x + 5
<=>
x = [14 +/-sqrt(196 - 160)]/16 = [14+/-6]/16
I.e. x is either 0.5 or 1.25
x^2–4x+11 = (3x-1)^2–4(3x-1)+11
<=>
x^2–4x = [9x^2–6x+1]-12x+4 = 9x^2 -18x + 5
<=>
0 = 8x^2 -14x + 5
<=>
x = [14 +/-sqrt(196 - 160)]/16 = [14+/-6]/16
I.e. x is either 0.5 or 1.25
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