Question

If f(x) = -x³, g(x) = 3x²-1, and h(x) = 2x + 5, what is the degree of [f og o h](x)?

2
03
05
06

Answer 1

(d) 6

Explanation:

The degree of a composition of polynomials is the product of the degrees of the contributing functions.

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f(g(h(x))) = -(3(2x+5)² -1)³

f(g(h(x))) = -1728x⁶ -25920x⁵ -161568x⁴ -535680x³ -996336x² -985680x -405224

The degree of (f∘g∘h)(x) is 6.

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3×2×1 = 6