If f(x) = 1 + x 2 and f(g(x)) = 1 + x 2 –2x 3 + x 4 , then …

Maths Functions, Limits, Continuity and Differentiability General Subjective Type

Published on: August 13, 2026

If f(x) = 1 + x 2 and f(g(x)) = 1 + x 2 –2x 3 + x 4 , then determine the function g(x) and find the domain of g(x).

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The correct answer is:

CHECK THE SOLUTION.

Sol. f (g(x)) = 1 + (g (x)) 2 = 1 + x 2 –2x 3 + x 4

⇒ (g(x)) 2 = x 2 (x 2 –2x + 1) = x 2 (x –1) 2 ⇒ g(x) = ±

∴ g(x) = ± x(x –1) = ± (x

2 –x)

Clearly domain of g(x) is R as x 2 (x –1) 2 ≥ 0 ∀ x ∈ R.

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