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in Sets, relations and functions by (50.3k points)

Let f(x) = 1 + x2. Find a function g(x) such that f(g(x)) = 1 + x2 – 2x3 + x4.

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Given f(g(x)) = 1 + x2 – 2x3 + x4

= 1 + (x4 – 2x3 + x2)

= 1 + x2(x2 – 2x + 1)

= 1 + x2(x – 1)2

= 1 + (x (x – 1))2

= g(x) = ±(x (1 – x))

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