Question 549606: Here is one I am having problems with as well.
Let g(x)=x+2/x-3 find g^-1, the domain, and the range...
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Here is one I am having problems with as well.
Let g(x)=x+2/x-3 find g^-1, the domain, and the range...
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g(x)=x+2/x-3
To find the domain, check for sqrts and zeros in the denominator. In this case, there are no sqrts involved but 3 is a zero, that is when x=3, g(x) becomes undefined. The domain is then, all real numbers except x≠3 or in set notation {x|x≠3} or interval notation (-∞,3) U (3,∞)
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To find the range, interchange x and y, then solve for y:
x=y+2/y-3
xy-3x=y+2
xy-y=3x+2
y(x-1)=3x+2
y=(3x+2)/(x-1)
Range: {y|y≠1} or (-∞,1) U (1,∞)
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Ans:
Domain of g(x): (-∞,3) U (3,∞)
Range of g(x):(-∞,1) U (1,∞)
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Domain and Range of g(x) become the Range and Domain of g^-1, that is, they are interchanged.
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