subject: Algebra Domain Expressions [print this page] Introduction to algebra domain expressions:
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.
Example Problems on Algebra Domain Expressions:
Exampl : 1
Find the domain function f that defined by f (x) = -1 / ( x + 8)
Solution:
To find the domain equate denominator to zero
x + 8 = 0
x = -8
Therefore the domain function f is the set of all values of x in the interval (-infinity, -8) U (-8, +infinity)
Example : 2
Find the domain function f that defined by f(x) = x^2 + 2.
Solution:
The function f(x) = x^2 + 2 is defined for all real values of x.
Hence, the domain function of f(x) is "all real values of x".
Since x^2 is never negative, x^2 + 2 is never less than 2
Example : 3
Find the domain function f that defined by f(t) = (1)/(t + 2)
Solution:
The function f(t) = (1)/(t + 2) is not defined for t = -2, as this value requires division by zero.
Hence the domain function of f(t) is "all real numbers except -2"
Also, no matter how large or small t becomes, f(t) will never be equal to zero
Example : 4
Find the domain function f that defined by f(x) = x^2 + 4 for x > 2
Solution:
The domain function f(x) has a domain of "all real numbers, x > 2" by definition.
We are told that the height x, in meters, of a certain projectile as a function of time t, in seconds, is h = 20t 4.9t2 . Find the domain function that defined by x(t).
Solution:
Generally, negative values of time do not have any meaning. Also, we need to assume that the projectile hits the ground and then stops - it does not go underground.
So we need to calculate when it is going to hit the ground. When x = 0.
So we solve:
20t 4.9t2 = 0
Factoring gives:
(20 4.9t)t = 0
This is true when
t = 0 s,
or
t = 20/4.9 = 4.082 s
Hence, the domain of the function x is
"all real values of t such that 0 t 4.082"
Practice Problems on Algebra Domain Expressions:
Practice problem:- 1
Find the domain of function f defined by f (x) = sqrt (-x + 9)
[Answer: Domain of function f is the set of all values of x in the interval (-infinity , 9 ) ]
Practice problem:- 2
Find the domain of function f defined by f (x) = sqrt( -x + 2) / [(x + 1)(x + 9)]
[Answer: domain of function f is the set of all values of x in the interval (-infinity , -9) U (-9 , -1) U (-1 , 2 ) ]