+20 Use the graph below to answer the following questions.
Will the inverse of f(x) be a function? How can you tell?
Using the above graph determine the domain and range of f(x) and the domain and range of f –1(x).
Determine a mapping of the form (x, y) --> (__, __) for the inverse of a relation. Explain how you determined this mapping.
+118677 The inverse of funtion x cannot be a function because for one segment of f(x)=-2 The inverse of that is just -2
I mean for the function For -3<=x<=-1 f(x)=-2
the inverse would be when x=-2 \(f^{-1}(2)\) can be any number between -3 and -1
Hence there is no unique value of \(f^{-1}(2) \) Hence \(f^{-1}(x)\) is not a function.
f(x) domain [-3,5] range [-2,3]
\(f^{-1}(x)\) domain [-2,3] range [-3,5]
I assume for the last bit
(x,y) --> (y,x) becasue the inverse of a function is its reflection about the line y=x
Here is a mapping
