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Domain-Range

Probability Introduction :

Domain and Range:

    Let \(f: A\mapsto B\) is function. A is called the Domain of f.

  Generally domain is the set of all numbers for which the formula makes sense

and defines a real number.

 Examples of domain :

1) y=2x  find domain.

Sol)    y= 2x  for all real values of x, y defines so domain is all reals.

In set notation Domain=(-\(\infty\), \(\infty\))

2) y=\(\sqrt{x-4}\) find domain.

Sol)  y=\(\sqrt{x-4}\)

    \(\sqrt{x-4}\) is real number when x-4 \(\geq\) 0 .

     x \(\geq\) 4

   Hence the domain of the function is [4, \(\infty\)).

3) y=\(\frac{x-3}{x+2}\) Find domain.

Sol)   \(\frac{x-3}{x+2}\) defines when denominator is not zero.

             x+2 \(\neq\) 0 .

               x\(\neq\) -2

     Given function defines for all real  x except -2 .

     Hence the domain is \((-\infty, -2) \cup  (-2 , \infty)\).

    


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