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100 Points! Algebra question. Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Thank you!

100 Points! Algebra question. Use synthetic substitution to find f(-3) and f(4) for-example-1
User Chickens
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Answer:

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537

What is a function

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

By substitution:

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.

User Michael Johansen
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