Theory of Intelligence
11TH•Mathematics•Functions And Graphs•Question 1

Overview

Given that:

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Given:

f(x)=x2−1f(x) = x^2 - 1

Replace xx with (x2+3)(x^2 + 3):

f(x2+3)=(x2+3)2−1=((x2)2+2(x2)(3)+32)−1=x4+6x2+9−1=x4+6x2+8\begin{aligned} f(x^2 + 3) &= (x^2 + 3)^2 - 1 \\ &= ((x^2)^2 + 2(x^2)(3) + 3^2) - 1 \\ &= x^4 + 6x^2 + 9 - 1 \\ &= x^4 + 6x^2 + 8 \end{aligned} f(x2+3)=x4+6x2+8\boxed{f(x^2 + 3) = x^4 + 6x^2 + 8}

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