Multiple Choice
Given the functions and , calculate
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3. Functions & Graphs
Function Operations
Multiple Choice
Given the functions and , find and fully simplify
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Verified step by step guidance1
First, understand that h(x) and k(x) are two functions, and we need to find the product h ⋅ k(x), which means multiplying h(x) by k(x).
Write down the expressions for h(x) and k(x): h(x) = 2x^3 - 4 and k(x) = x^2 + 2.
To find h ⋅ k(x), multiply the two functions: (2x^3 - 4) * (x^2 + 2).
Use the distributive property to expand the product: 2x^3 * x^2 + 2x^3 * 2 - 4 * x^2 - 4 * 2.
Simplify each term: 2x^5 + 4x^3 - 4x^2 - 8. Combine like terms if necessary to get the final simplified expression.
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