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IBA Entry Test Preparation Material IBA Entry Test PreparationFunction Function: An equationwill be a function if for any x in the domain of the equation, the equation will yield exactly one value of y .For example, Q. 2 1 y x is a function or not?Solution: 2 1 y x can also be written as, 2 ()1 f x x Put 0 x we have 2 (0)011 f For 0 x we have exactly one value of () f x that is, 1.Put 1 x we have 2 (1)112 f For 1 x we have exactly one value of () f x that is, 2In the above equation, for any x in the domain of the equation, the equation will yield exactly one value of y. Hence, it is a function.Q. 2 1 y x is a function or not?Solution:Put 0 x in the above equation, 2 01 y 2 1 y 1 y So, for 0 x we have 2 different values of y . Hence it is not a function. Even and Odd Function Even Function Suppose () f x is a function, And if, ()() f x f x then the function is EVEN. Odd Function Suppose () f x is a function, And if, ()() f x f x then the function is ODD.For example,Q. Whether the Function 2 () f x x is Even or Odd?SolutionReplace x by x . 22 ()() f x x x Hence, ()() f x f x The function is Even. IBA Entry Test Preparation MaterialQ. Whether the Function 3 () f x x is Even or Odd?SolutionReplace x by x . 33 ()() f x x x Hence, ()() f x f x The function is Odd. Domain and Range of a Function Domain of a Function The Domain of a function is the set of all values that could be put into a function and have the function exists and have a real number of value.So, for the domain we need to avoid division by zero, square root of negative numbers, logarithm of zeroes and negative numbers. Range of a Function The range of a Function is simply the set of all possible values that a function can take.For example,Q. Find Domain and Rangeof ()27 f x x SolutionIn this function, we can put any value of x .Domain: (,) Range: (,) Q. Find Domain and Range of ()42 f x x .SolutionWe could NOT have negative value in square root. So, 42 x 0 420422412 x x x x Hence, domain: 1[,)2 Range: [0,) IBA Entry Test Preparation MaterialQ. Find Domain and Range of 1()1 f x x Q.76 IBA Entry Test BBA -2010SolutionWe cannot have 1 in the denominator for which the function is,111()1110 f x x does not existsHence, Domain: All numbers except 1.Range: For different values of x the function will take different values.For 0 x , ()1 f x For 1 x , 12 For 2 x , ()1 f x Hence, Range could be any Real ValueAnswer: (D) The set of all Real Values.
