Questions: The graphs of f and g are shown. Evaluate the function at the given value of x, if possible. (f ⋅ g)(-3) ⋅ f(g-3) → f(z) → a. -3 b. 0 f(-3) c. 1 d. -2

Transcript text: The graphs of $f$ and $g$ are shown. Evaluate the function at the given value of $x$, if possible. \[ (f \cdot g)(-3) \cdot f(g-3) \rightarrow f(z) \rightarrow \] a. -3 b. 0 $f(-3)$ c. 1 d. -2

Solution

Solution Steps

Step 1: Evaluate g(-3)

First, we need to find the value of $ g(-3) $ from the graph. Looking at the graph, when $ x = -3 $, the value of $ g(x) $ is 2.

Step 2: Substitute g(-3) into f(x)

Next, we substitute $ g(-3) $ into $ f(x) $. Since $ g(-3) = 2 $, we need to find $ f(2) $.

Step 3: Evaluate f(2)

Now, we find the value of $ f(2) $ from the graph. Looking at the graph, when $ x = 2 $, the value of $ f(x) $ is 0.

Final Answer

The final answer is $ f(g(-3)) = f(2) = 0 $.

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