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What is (f*g)(x) ? {:[f(x)=5x+6],[g(x)=2x+1]:} Write your answer as a polynomial or a rational function.

What is (f∗g)(x)(f*g)(x)?\newlinef(x)=5x+6f(x)=5x+6 \newlineg(x)=2x+1g(x)=2x+1\newlineWrite your answer as a polynomial or a rational function.

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Full solution

Q. What is (f∗g)(x)(f*g)(x)?\newlinef(x)=5x+6f(x)=5x+6 \newlineg(x)=2x+1g(x)=2x+1\newlineWrite your answer as a polynomial or a rational function.
  1. Define functions and operation: Define the functions and the operation needed.\newlineWe need to multiply the functions f(x)f(x) and g(x)g(x).\newlinef(x)=5x+6f(x) = 5x + 6, g(x)=2x+1g(x) = 2x + 1.\newlineWe will find (f∗g)(x)(f*g)(x) by multiplying these two functions.
  2. Multiply functions: Multiply the functions.\newline(f∗g)(x)=(5x+6)(2x+1)(f*g)(x) = (5x + 6)(2x + 1)\newline=5x(2x)+5x(1)+6(2x)+6(1)= 5x(2x) + 5x(1) + 6(2x) + 6(1)\newline=10x2+5x+12x+6= 10x^2 + 5x + 12x + 6\newline=10x2+17x+6= 10x^2 + 17x + 6

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