Final answer:
To find g(f(-1)), calculate f(-1) first, which is 1. Then, use f(-1) to evaluate g(1) which requires finding f(0) that equals to 3. Finally, compute g(f(-1)) as -3 + 5, resulting in 2.
Step-by-step explanation:
To find the value of g(f(-1)), we first need to determine the output of f(-1). Then substitute this output into the function g(x).
Step 1: Calculate f(-1). Using the definition of the function f(x) = 2x + 3, substitute -1 for x:
f(-1) = 2(-1) + 3 = -2 + 3 = 1.
Step 2: Find g(f(-1)). According to the function definition, g(x) = -f(x - 1) + 5, substitute f(-1) which we determined to be 1 into this function:
g(1) = -f(1 - 1) + 5 = -f(0) + 5.
Step 3: Now compute f(0). Again using the formula for f(x):
f(0) = 2(0) + 3 = 3.
Step 4: Combine these results to evaluate g(f(-1)):
g(f(-1)) = g(1) = -f(0) + 5 = -(3) + 5 = -3 + 5 = 2.
Therefore, the value of g(f(-1)) is 2.