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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.

 Feb 18, 2022
 #1
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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

 

 Feb 19, 2022

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