Question

3. Two functions f and g are defined on the set of real numbers, R, by f:x→x²+2 and g:x→1/(x+2), x≠−2. Find the domain of (g∘f)⁻¹.

Accepted Answer

(g∘f)(x) = g(x²+2) = 1/(x²+2+2) = 1/(x²+4). Let y=1/(x²+4); solving for x gives x=√[(1−4y)/y], so (g∘f)⁻¹(x) = √[(1−4x)/x].
The domain requires (1−4x)/x ≥ 0, i.e. 0 < x ≤ 1/4.

WAEC Further Mathematics 2022 Theory — Question 3

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