CAT Functions - Answers

Answers to questions on Functions posted more than a while ago here

1. Give the domain and range of the following functions

i. f(x) = x² + 1
Domain = All real numbers (x can take any value)
Range  [1, infinity). Minimum value of x² is 0.

 

ii. g(x) = log (x + 1)

Domain = Log of a negative number is not defined so (x + 1) > 0 or x > -1

Domain ( -1, infinity)

Range = (-infinity, +infinity)

Note: Log is one of those beautiful functions that is defined from a restricted domain to all real numbers. Log 0 is also not defined. Log is defined only for positive numbers

 

iii. h(x) = 2^xDomain - All real numbers.

Range = (0, infinity)

 

The exponent function is the mirror image of the log function. 

 

iv. f(x) = 1/ (x+1)

Domain = All real numbers except -1

Range = All real numbers except 0
 

v. p(x) = | x + 1|
Domain = All real numbers 

Range = [0, infinity) Modulus cannot be negative

 

vi. q(x) = [2x], where [x] gives the greatest integer less than or equal to x

Domain = All real numbers

Range = All integers

 

The range is NOT the set of even numbers. [2x] can be odd. [2*0.6] = 1. It is very important to think fractions when you are substituting values.

 

Best wishes for CAT 2012.