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MATHMAA

# Domain-Range

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 $$(-\infty, -2) \cup (-2 , \infty)$$.