Question

If $f(x^2 - 1) = x^4 - 7x^2 + k_1$ and $f(x^3 - 2) = x^6 - 9x^3 + k_2$, then the value of $(k_2 - k_1)$ is:

Accepted Answer

C. Let $x^2 - 1 = 0 \implies x^2 = 1$. $f(0) = (1)^2 - 7(1) + k_1 = k_1 - 6$. Let $x^3 - 2 = 0 \implies x^3 = 2$. $f(0) = (2)^2 - 9(2) + k_2 = k_2 - 14$. Equating both expressions for $f(0)$: $k_1 - 6 = k_2 - 14 \implies k_2 - k_1 = 8$.

Algebraic Functional Equations

Explanation

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