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Find f(x), if g(x) = x2 + x – 2 and (gof) (x) = 4x2 – 10x + 4 |
Answer» g(x) = x2 + x – 2 (gof) (x) = 4x2 – 10x + 4 = (2x – 3)2 + (2x – 3) – 2 = g(2x – 3) = g(f(x)) ∴ f(x) = 2x – 3 (gof) (x) = 4x2 – 10x + 4 = (-2x + 2)2 + (-2x + 2) – 2 = g(-2x + 2) = g(f(x)) ∴ f(x) = -2x + 2 |
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