I really need help understanding ho to solve combination functions
here is a specific problem I am struggling with.
Let f(x) = x - 2 and g(x) = x^2 - 7x - 9. Find f(g(-1)).
g(x) = x^2 - 7x - 9
g(-1) = (-1)^2 - 7*(-1) - 9 = -1
F(g(-1)) = F(-1)
F(x) = x - 2
F(-1) = -1 - 2 = -3.
To solve this problem, we need to find f(g(-1)), which means we need to find the composition of the two functions. Here are the steps to solve the problem:
Step 1: Find g(-1)
Substitute -1 into the function g(x):
g(-1) = (-1)^2 - 7(-1) - 9
g(-1) = 1 + 7 - 9
g(-1) = -1
Step 2: Substitute g(-1) into f(x)
Substitute -1 into the function f(x):
f(-1) = -1 - 2
f(-1) = -3
Therefore, f(g(-1)) = -3.
In summary, to find f(g(-1)), we first plugged -1 into the function g(x) to find g(-1), and then we substituted g(-1) into the function f(x) to find f(g(-1)). The final result is -3.