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Answer :
Final Answer:
When evaluated at x = -3, the function [tex]f(x) = 4x^4 + 5x^3 - 15x^2 - 45[/tex] takes the value 9.
Explanation:
To find f(-3), we simply substitute x = -3 into the function's expression:
[tex]f(-3) = 4(-3)^4 + 5(-3)^3 - 15(-3)^2 - 45\\f(-3) = 4 * 81 + 5 * -27 - 15 * 9 - 45\\f(-3) = 324 - 135 - 135 - 45\\f(-3) = 324 - 285\\f(-3) = 9[/tex]
Therefore, f(-3) = 9.
In conclusion, evaluating f(x) at x = -3 reveals its value as 9. This demonstrates that even negative inputs can yield positive function outputs, highlighting the dynamic nature of polynomial expressions. While finding f(-3) may seem like a simple substitution, it reinforces the importance of understanding the underlying function's structure and applying basic algebraic principles.
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