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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=x+4g(x) = x + 4\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=x+4g(x) = x + 4\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify Formula: Identify the formula for (f∗g)(x)(f * g)(x).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Multiply Functions: We have:\newlinef(x)=5xf(x) = 5x\newlineg(x)=x+4g(x) = x + 4\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=5x∗(x+4)(f * g)(x) = 5x * (x + 4)
  3. Distribute 5x5x: Distribute 5x5x across the terms in the parentheses.\newline(f⋅g)(x)=5x⋅x+5x⋅4(f \cdot g)(x) = 5x \cdot x + 5x \cdot 4
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=5x2+20x(f \cdot g)(x) = 5x^2 + 20x
  5. Express Answer: Express your answer as a simplified polynomial.\newlineThe polynomial 5x2+20x5x^2 + 20x is already in its simplest form.

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