Composition of even and odd functions from graphs Assume ƒ is an even function and g is an odd function. Use the (incomplete) graphs of ƒ and g  in the figure to determine the following function values. <IMAGE>


a. ƒ(g(-2))

Verified step by step guidance

1. Step 1: Understand the properties of even and odd functions. An even function satisfies f(x) = f(-x) for all x in its domain, while an odd function satisfies g(x) = -g(-x).
2. Step 2: Identify the value of g(-2) using the property of odd functions. Since g is odd, g(-2) = -g(2).
3. Step 3: Use the graph of g to find g(2). Locate the point on the graph where x = 2 and determine the corresponding y-value, which is g(2).
4. Step 4: Calculate g(-2) using the value found in Step 3. Since g(-2) = -g(2), take the negative of the y-value found for g(2).
5. Step 5: Use the graph of f to find f(g(-2)). Locate the point on the graph of f where x equals the value of g(-2) and determine the corresponding y-value, which is f(g(-2)).