If \( f(x) = x - 1 \), and \( g(f(x)) = 3 + 2x - x^2 + x^3 \), which of the following gives a correct expression for \( g(x) \)?
Question and options
If , and , which of the following gives a correct expression for ?
Answer and explanation
Correct answer: B - \(x^3 + 2x^2 + 3x + 5\)
Let t = x - 1, so x = t + 1. g(t) = 3 + 2(t+1) - (t+1)^2 + (t+1)^3 = t^3 + 2t^2 + 3t + 5.
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