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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5x+1f(x) = 5x + 1\newlineg(x)=2x2g(x) = 2x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5x+1f(x) = 5x + 1\newlineg(x)=2x2g(x) = 2x^2\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. Given Functions: We have:\newlinef(x)=5x+1f(x) = 5x + 1\newlineg(x)=2x2g(x) = 2x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(5x+1)∗(2x2)(f * g)(x) = (5x + 1) * (2x^2)
  3. Multiply Functions: Distribute 5x+15x + 1 over 2x22x^2 to find the product.\newline(f∗g)(x)=5x∗2x2+1∗2x2(f * g)(x) = 5x * 2x^2 + 1 * 2x^2
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=10x3+2x2(f * g)(x) = 10x^3 + 2x^2\newlineThis is the simplified polynomial form of (f∗g)(x)(f * g)(x).

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