Question

5* the function f is defined by f(x) = x⁵ + 4x⁴ + x for all values of x. the function g is defined by g(x) = 4x³ − 17x² − 74 for all values of x. what is the product of f(−3) and g(5)? a) −15 b) 78 c) 79 d) 564

Explanation:

Step1: Calculate \( f(-3) \)

Given \( f(x) = x^5 + 4x^4 + x \) (assuming the missing term is \( x \) or a typo, but we proceed with given structure). Substitute \( x = -3 \):

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Step2: Calculate \( g(5) \)

Given \( g(x) = 4x^3 - 17x^2 - 74 \). Substitute \( x = 5 \):

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Step3: Find the product

Multiply \( f(-3) \) and \( g(5) \): \( 78 \times 1 = 78 \) (Wait, earlier \( g(5) \) calculation: \( 500 - 425 = 75; 75 - 74 = 1 \). Correct. \( f(-3) = 78 \), so \( 78 \times 1 = 78 \))

Answer:

B. 78