Domain all the Real Numbers

In mathematics, the domain of definition or simply the domain of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or "value" for each member of the domain. For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0.(Source: Wikipedia)

Domain all the real values - Example problems:

Example problem: 1
Find the domain function of f that can be defined by f (x) = -1 / ( x + 10)
Solution:
  To find the domain equate denominator to zero
  x + 10 = 0
  x = -10
Therefore the domain function of f is the set of all real values of x in the interval is(-infinity, -10) U (-10, +infinity)
Example problem: 2
 Find the domain function of f that can be defined by f(x) = x² + 6.
Solution:
 The function f(x) = x² + 6 is defined for all real values of x.
 Hence, the domain function of f(x) is the function of  "all real values of x".
 Since x² is never negative, x² + 6 is never less than 2
Example problem: 3
 Find the domain function of f that can be defined by f(t) = (1)/(t + 6)
Solution:
 The function f(t) = (1)/(t + 6) is not defined for t = -6, as this value requires division by zero.
 Hence the domain function of f(t) is the function of all the real numbers except -6
 Also, no matter how large or small t becomes, f(t) will never be equal to zero

Domain all the real values - Practice problems:

Practice problem:- 1
Find the domain of function of f that can be defined by f (x) = sqrt (-x + 16)
[Answer: Domain of function f is the set of all values of x in the interval (-infinity, 16) ]
Practice problem:- 2
Find the domain of function f defined by f (x) = sqrt( -x + 4) / [(x + 2)(x + 8)]
[Answer: domain of function f is the set of all values of x in the interval   (-infinity, -8) U    (-8, -2) U (-2, 4)]