Final answer:
The student's questions involve finding values of functions and compositions given the graphs of the functions. Each part requires a different procedure - finding a value that corresponds to a given y-value, composing two functions, or finding an inverse function value.
Step-by-step explanation:
To evaluate the functions given in the question, we need to understand the concepts of inverse functions, function composition, and the use of function graphs.
A) f⁻¹(0)
Finding f⁻¹(0) means we are looking for the x such that f(x) = 0. You would look at the graph of y = f(x) and find where the y-value is 0. Then, you can read the corresponding x-value which is f⁻¹(0).
B) f(g(x))(2)
To find f(g(x))(2), first evaluate g(2) to find the output of g at x = 2, which will give you some value 'a'. Then, plug that 'a' into the function f to find f(a).
C) f⁻¹(g(0))
f⁻¹(g(0)) requires us to first evaluate g(0). Once you have that value, say 'b', find the x-value corresponding to f(x)=b on the graph of f. That x-value is your answer.
D) g(f⁻¹(x))(2)
Lastly, evaluating g(f⁻¹(x))(2) involves first finding f⁻¹(2), say 'c', which is the x-value for which f(x) = 2. Then, take g(c) by finding the y-value of g at that x-value.