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We are given the function:
Domain:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
In case of fractions, we must not have the denominator as zero , otherwise the function will become undefined.
So equating denominating equal to zero to find restriction.
x=6
So at x=6 , the function becomes undefined.
So domain is all real numbers except x=6.
Range:
For a fraction, we find domain of inverse function and that gives the range.
replacing g(x) by y
switching y by x and x by y
solving for y,
Now here we find domain of this function.
Again for a fraction denominator cannot be zero
So range is :
g(x) >0 and g(x) <0