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Find (f∘g)(0)(f \circ g)(0).\newlinef(x)=6xf(x) = 6x\newlineg(x)=x2+4xg(x) = x^2 + 4x\newline(f∘g)(0)=(f \circ g)(0) = ____

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Composition of linear and quadratic functions: find a valueright chevron icon

Full solution

Q. Find (f∘g)(0)(f \circ g)(0).\newlinef(x)=6xf(x) = 6x\newlineg(x)=x2+4xg(x) = x^2 + 4x\newline(f∘g)(0)=(f \circ g)(0) = ____
  1. Find g(0)g(0): question_prompt: What is the value of (f∘g)(0)(f \circ g)(0) for the given functions f(x)f(x) and g(x)g(x)?
  2. Calculate f(g(0))f(g(0)): First, let's find g(0)g(0) by plugging in 00 into g(x)g(x). g(0)=02+4⋅0=0g(0) = 0^2 + 4\cdot0 = 0.
  3. Determine (f∘g)(0)(f \circ g)(0): Now, we plug g(0)g(0) into f(x)f(x) to get f(g(0))f(g(0)). f(g(0))=f(0)=6×0=0f(g(0)) = f(0) = 6\times0 = 0.
  4. Determine (f∘g)(0)(f \circ g)(0): Now, we plug g(0)g(0) into f(x)f(x) to get f(g(0))f(g(0)). f(g(0))=f(0)=6⋅0=0f(g(0)) = f(0) = 6\cdot0 = 0. So, (f∘g)(0)(f \circ g)(0) is equal to f(g(0))f(g(0)), which we found to be 00.

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