Given function is f(x)=3−xx−2 .
Now given function has numerator and denominator both continuous and denominator is 3−x.
So given function is not defined when 3−x=0⟹x=3.
So, posible domain where function is defined should not contains x=3.
Hence Largest possible domain is D = (−∞,3)∪(3,∞).
Now when x∈(−∞,3)⟹x<3⟹3−x>0 and when x∈(3,∞)⟹3−x<0.
Also, for x∈(3,∞),x−2∈(1,∞) and so f(x)∈(−∞,−1).
And for x∈(−∞,3),f(x)=−1+3−x1∈−1+(0,∞)∈(−1,∞).
So, Range of given function is (−∞,−1)∪(−1,∞).
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