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Given the function f(x)=-x-5x^(2), then what is f(-3x) as a simplified polynomial? Answer:

Given the function f(x)=−x−5x2 f(x)=-x-5 x^{2} , then what is f(−3x) f(-3 x) as a simplified polynomial?\newlineAnswer:

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Full solution

Q. Given the function f(x)=−x−5x2 f(x)=-x-5 x^{2} , then what is f(−3x) f(-3 x) as a simplified polynomial?\newlineAnswer:
  1. Write Function: First, let's write down the function we need to work with. f(x)=−x−5x2f(x) = -x - 5x^2
  2. Replace xx in f(x)f(x): Now, we need to replace every xx in f(x)f(x) with −3x-3x to find f(−3x)f(-3x).
    f(−3x)=−(−3x)−5(−3x)2f(-3x) = -(-3x) - 5(-3x)^2
  3. Simplify Expression: Simplify the expression by calculating the operations inside the parentheses. f(−3x)=3x−5(9x2)f(-3x) = 3x - 5(9x^2)
  4. Multiply Constant: Now, multiply the constant outside the parentheses by each term inside the parentheses.\newlinef(−3x)=3x−45x2f(-3x) = 3x - 45x^2

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