Questions: The graph of f(x) and a table of values for g(x) are given below. Use them to evaluate the given statements. x 0 1 2 3 4 5 6 7 8 9 g(x) 8 7 2 0 3 1 6 9 5 4 (f+g)(3)=3 (f g)(0)=-4 (g ∘ f)(5)= (g ∘ g)(0)=

The graph of f(x) and a table of values for g(x) are given below. Use them to evaluate the given statements. x 0 1 2 3 4 5 6 7 8 9 g(x) 8 7 2 0 3 1 6 9 5 4 (f+g)(3)=3 (f g)(0)=-4 (g ∘ f)(5)= (g ∘ g)(0)=
Transcript text: The graph of $f(x)$ and a table of values for $g(x)$ are given below. Use them to evaluate the given statements. \begin{tabular}{|c|l|l|l|l|l|l|l|l|l|l|} \hline$x$ & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline$g(x)$ & 8 & 7 & 2 & 0 & 3 & 1 & 6 & 9 & 5 & 4 \\ \hline \end{tabular} \[ (f+g)(3)=3 \] \[ \begin{array}{l} (f g)(0)=-4 \\ (g \circ f)(5)= \end{array} \] \[ (g \circ g)(0)= \]
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Solution

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Solution Steps

Step 1: Evaluate \( (f + g)(3) \)

To find \( (f + g)(3) \), we need to evaluate \( f(3) \) and \( g(3) \) and then add them together.

  • From the graph, \( f(3) = 3 \).
  • From the table, \( g(3) = 0 \).

So, \( (f + g)(3) = f(3) + g(3) = 3 + 0 = 3 \).

Final Answer

\( (f + g)(3) = 3 \)

Step 2: Evaluate \( (fg)(0) \)

To find \( (fg)(0) \), we need to evaluate \( f(0) \) and \( g(0) \) and then multiply them together.

  • From the graph, \( f(0) = -4 \).
  • From the table, \( g(0) = 8 \).

So, \( (fg)(0) = f(0) \cdot g(0) = -4 \cdot 8 = -32 \).

Final Answer

\( (fg)(0) = -32 \)

Step 3: Evaluate \( (g \circ f)(5) \)

To find \( (g \circ f)(5) \), we need to evaluate \( f(5) \) first and then use that result to find \( g \) of that value.

  • From the graph, \( f(5) = 5 \).
  • From the table, \( g(5) = 6 \).

So, \( (g \circ f)(5) = g(f(5)) = g(5) = 6 \).

Final Answer

\( (g \circ f)(5) = 6 \)

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