a) is saying what value of f(x) will result in an answer where the inverse has a domain of 1. This sounds more complex than it is, because the range of the function is the domain of the inverse, all they're saying is what value of x will give you a y value of 1. Obviously there are two values for x that when squared give you 1. They would be positive and negative 1.
b) Okay, so just reword this to be what x values for f(x) will give you y values greater than 0 and less than 1. Well and So you know that x values between 0 and 1 will give you y values between 0 and 1. Now, because the sign is greater than, but not equal to, and less than but not equal to, you know that x can never actually be 0 or 1. So the answer would be (0, 1) in parentheses.
c) Right, so what x values when plugged into the equation will give you y values that are greater than 4?