If f: R->R is defined by f(x)= x^2 - 3 x + 2, find f[f(x)].
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Step-by-step explanation:
Given, f: R->R is defined by f(x)= x^2 - 3 x + 2
f[f(x)]. = f[x²-3x+2]
= ( x²-3x+2 )² - 3(x²-3x+2) + 2
= (x²)² + (3x)² + (2)² + 2(x²)(3x) + 2(3x)(2) + 2(2)(x²) - 3x² + 9x - 6 + 2
= x^4 + 9x² + 4 + 6x³ + 12x + 4x² - 3x² + 9x - 4
= x^4 + 6x³ + 10x² + 21x
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