SOLUTION: for the one-to-one function f(x)= 2/x-4 Find the inverse f^-1 Find the domain and range of f Find the domain and range of f^-1

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Question 206027: for the one-to-one function f(x)= 2/x-4
Find the inverse f^-1
Find the domain and range of f
Find the domain and range of f^-1
Answer by mickclns(59)   (Show Source): You can put this solution on YOUR website!

To find the inverse function of a function, replace x by y and y (or f(x) ) by x and solve for y
 
      add 4 to each side
     change the left side to a fraction and flip both sides
     multiply both sides by 2, then switch sides so y (the inverse of f(x) ) is on the left

 
Here is a graph of f (red) and its inverse (green, the vertical line at -4 should be ignored, it is not part of either function). Also, graphed is the line y=x ... a function and its inverse are always mirror images of one another across this line, which you can see for the green and the red here.

 
 
The domain of f is all real numbers except 0 (because x = x-0 is in the denominator makes f(x) undefined).
The range of f is all real numbers except -4 ... for -4 to be the value of y, would have to be 0 which means x would have to be infinitely large, but no real number is infinitely large.
The domain of is all real numbers except -4 (because x+4 = -4+4 is in the denomiator and makes undefined).
The range of is all real numbers except 0 ... for 0 to be the value of y, would have to be 0 which means x-4 (and therefore x) would have to be infinitely large, but no real number is infinitely large.
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