Question

assume f is an even function and g is an odd function. assume f and g are defined for all real numbers. use the table to evaluate the given compositions.

x	1	2	3	4
g(x)	-3	-4	-1	-2

a. f(g(-1))
b. g(f(-4))
c. f(g(-3))
d. f(g(-2))
e. g(g(-1))
f. f(g(0) - 1)
g. f(g(g(-2)))
h. g(f(f(-4)))
i. g(g(g(-1)))

a. f(g(-1)) = \square

Explanation:

Step1: Use odd function property for g(-1)

Since \( g \) is odd, \( g(-x) = -g(x) \). So \( g(-1) = -g(1) \). From the table, \( g(1) = -3 \), so \( g(-1) = -(-3) = 3 \).

Step2: Evaluate f(g(-1))

Now \( g(-1) = 3 \), so we need \( f(3) \). From the table, \( f(3) = 2 \).

Answer:

2