The question is about Domain and Range. Several functions arre given and we need to find out the range and domain of them. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 5: Give the domain and range of the following functions:

- f(x) = x
^{2}+ 1 - g(x) = log(x + 1)
- h(x) = 2
^{x} - f(x) = \\frac{1}{x+1}\\)
- p(x) = |x + 1|
- q(x) = [2x], where [x] gives the greatest integer less than or equal to x

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A. f(x) = x^{2} + 1

Domain = All real numbers (x can take any value)

Range [1, ∞). Minimum value of x^{2} is 0.

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

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

Domain ( -1, ∞)

Range = (-∞, +∞)

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

C. h(x) = 2^{x} Domain - All real numbers.

Range = (0, ∞)

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

D. f(x) = \\frac{1}{x + 1}\\)

Domain = All real numbers except -1

Range = All real numbers except 0.

E. p(x) = |x + 1|

Domain = All real numbers

Range = [0, ∞) Modulus cannot be negative

F. 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.

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