You should really put 4-x in parentheses (or use LaTeX):FlopperJr said:Homework Statement
The function f:x→ 4-x2 for the domain x≤0. Find the inverse of is denoted by f-1 and state the domain and range of f-1.
Homework Equations
Set equation to 0 and solve for x to find inverse. The D and R is going to be switched for the inverse..?
The Attempt at a Solution
I think I have found the inverse and range for this problem:
f-1(x) = -√4-x
and has a range of y≤0 (which was given in problem)
not sure of range. Are my solutions correct?
FlopperJr said:No, That is my problem. I tried but I keep getting wrong answer. 4-x^2=0
x=+/-2
SammyS said:How would you describe the graph of y = 4-x2 ?
The domain of the inverse function f-1 is all real numbers less than or equal to 0 (x≤0).
The range of the inverse function f-1 is all real numbers less than or equal to 0 (y≤0).
The domain of f-1 is the same as the range of the original function f, and vice versa. This is because the inverse function is essentially the "flipped" version of the original function, so the x-values that were in the range of f become the y-values in the domain of f-1.
Yes, it is possible for the inverse function f-1 to have a different domain and range than the original function f. This can happen when the original function f is not one-to-one, meaning that more than one input can produce the same output. In this case, the inverse function f-1 may have a restricted domain and range in order to maintain its one-to-one nature.
If the inverse function f-1 has a restricted domain and range, you can graph it by first graphing the original function f, then reflecting it over the line y=x. Next, you can use the restricted domain and range to "cut off" any parts of the graph that fall outside of the given range. This will give you the graph of the inverse function f-1 with the restricted domain and range.