IBA Test Prep Material

 

IBA Entry Test Preparation Material

IBA Entry Test Preparation Function Function: An equation equation will be a function function if for any  x in the domain of the equation, the equation will yield exactly one value of  y . For example, Q.  y  x 2  1 is a function or not? Solution:  y  x 2  1 can also be written as,  f ( x)  x 2  1 Put  x   0 we have  f  (0  )  02  1  1  f ( x ) that is, 1.

For  x   0 we have exactly one value of

Put  x   1 we have  f  (1  )  12  1  2 For  x   1 we have exactly one value of  f ( x ) that is, 2 In 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.  y 2  x  1 is a function or not? Solution: Put  x   0 in the above equation,  y 2   0  1  y 2 

1

 y    1 So, for  x   0 we have 2 different values of  y . Hence it is not a function.

Even and Odd Function Even Function

Suppo posse  f ( x) is a function, And if,  f ( x)  f ( x) then the function is EVEN. Odd Function

Suppo posse  f ( x) is a function, And if,  f (  x)   f ( x) then the function is ODD. For example, Q. Whether the Function  f ( x)  x 2 is Even or Odd? Solution Replace  x  by  x .  f (  x)  ( x ) 2  x 2 Hence,  f (  x)  f ( x) The function is Even.

 

IBA Entry Test Preparation Material Q. Whether the Function  f ( x)  x3 is Even or Odd? Solution Replace  x  by  x .  f (  x)  ( x )3   x 3 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 Fun ction is simply the set of all possible values that a function can take. For example, Q. Find Domain and Range of  f ( x)  2 x  7 Solution In this function, we can put any value of  x . Domain: (, ) Range: (, ) Q. Find Domain and Range of  f ( x)  4 x  2 . Solution We coul could d NOT NOT have have nega negati tive ve val value ue in sq squa uare re root root.. So, So, 4 x  2 4 x  2  0 4 x



 x   x 

2 2

4 1 2

1 Hence, domain: [ , ) 2 Range: [0, )



0

 

IBA Entry Test Preparation Material

Q. Find Domain and Range of  f ( x) 

1  x  1

Q.76 IBA Entry Test BBA -2010

Solution We cannot have 1 in the denominator for which the function is, 1 1 1  f ( x )    does not exists  x  1 1  1 0 Hence, All numbers 1.  x the function Range: Domain: For different values ofexcept will take different values. For  x   0 ,  f ( x)   1 1 For  x   1 , 2 For  x   2 ,  f ( x)   1 Hence, Range could be any Real Value Answer: (D) The set of all Real Values.