Math Problem Statement

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Given f(x) = 4x^2 - 3 and g(x) = 3 - (1/2)x^2, find the following expressions: (a) (f ∘ g)(4), (b) (g ∘ f)(2), (c) (f ∘ f)(1), (d) (g ∘ g)(0).

Solution

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Math Problem Analysis

Mathematical Concepts

Composition of Functions
Quadratic Functions
Substitution

Formulas

f(x) = 4x^2 - 3
g(x) = 3 - (1/2)x^2
(f ∘ g)(x) = f(g(x))
(g ∘ f)(x) = g(f(x))

Theorems

Function Composition

Suitable Grade Level

Grades 9-11

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