SOLUTION: f(x)= x+4/x-2 find f^-1(y) So find the inverse. Then what is the range of f(x)?

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Question 917830: f(x)= x+4/x-2 find f^-1(y) So find the inverse. Then what is the range of f(x)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+f%28x%29=+%28x%2B4%29%2F%28x-2%29+
find f%5E-1%28y%29
since f%28x%29=y we have
+y+=+%28x%2B4%29%2F%28x-2%29 ...swap x and y
+x+=+%28y%2B4%29%2F%28y-2%29 .......solve for y
+x%28y-2%29+=+y%2B4+
+x%2Ay-2x+=+y%2B4+
+-2x-4+=+y-xy+
+-2x-4+=+y%281-x%29+
+%28-2x-4%29%2F%281-x%29+=+y+
+y=-2%28x%2B2%29%2F%28-%28x-1%29%29+
+y=2%28x%2B2%29%2F%28x-1%29+

the range of f%28x%29:
{ f element R : f%3C%3E1 }
(assuming a function from reals to reals)