Answer:
g and f are inverse functions because g(f(x)) = f(g(x)) = x
Step-by-step explanation:
Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

Now, let's find g(f(x)):

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

Swap x and y:

Solve for y:

Notice that we got g, which means f and g are inverse.
Answer: g(f(-1))=-22
Step-by-step explanation:
To find g(f(-1)), you want to first want to solve f(-1). Once you solved that, you plig the answer you get into g(x). Then, you will have your final answer.
f(-1)=-(-1)²+4(-1)-9 [exponent]
f(-1)=-1+4(-1)-9 [multiply]
f(-1)=-1-4-9 [subtract from left to right]
f(-1)=-14
We have found that f(-1)=-14. Now, we know in -14 into g(x) and solve.
g(-14)=(-14)-8 [subtract]
g(-14)=-22
Now, we know that g(f(-1))=-22.
Im pretty sure that means what is y when x is -5. the answer is 5