Question
The range of the function 
is-
- R
- R – {–1}
- R – {1}
- R – {2}
Hint:
The correct answer is: R – {–1}
To find the range of the given function.
Let f(x)=y,
2y−xy=2+x
2y−2=x(1+y)
y cannot take '-1' value as x is not defined for that value.
Hence, range of the given function will be R−{−1}
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If R be a relation '<' from A = {1, 2, 3, 4} to B = {1, 3, 5} i.e. (a, b) 
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If R be a relation '<' from A = {1, 2, 3, 4} to B = {1, 3, 5} i.e. (a, b) R iff a < b, then is
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Let R = {(x, y) : x, y A, x + y = 5} where A = {1, 2, 3, 4, 5} then
Hence, the given relation is not reflexive, symmetric and not transitive
Let R = {(x, y) : x, y A, x + y = 5} where A = {1, 2, 3, 4, 5} then
Hence, the given relation is not reflexive, symmetric and not transitive
Let 
be a relation defined by 
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Hence, the given relation is Reflexive, transitive but not symmetric.
Let be a relation defined by Then R is
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The relation R defined in N as aRb 
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Hence, the given relations is reflexive but not symmetric.
The relation R defined in N as aRb b is divisible by a is
Hence, the given relations is reflexive but not symmetric.
