SOLUTION: It was stated that a real function is a function whose domain
and codomain are subsets of the real numbers R. Most of the functions
used in calculus are real functions. Quite oft
Algebra.Com
Question 495875: It was stated that a real function is a function whose domain
and codomain are subsets of the real numbers R. Most of the functions
used in calculus are real functions. Quite often, a real function is given by a
formula or a graph with no specific reference to the domain or the codomain.
In these cases, the usual convention is to assume that the domain of the real
function f is the set of all real numbers x for which f(x) is a real number and that the codomain is R. For example, if we define the (real) function f
by,
f(x)=x/x-2,
we would be assuming that the domain is the set of all real numbers that are not equal to 2.
Determine the domain and range of each of he following real functions.
a.)The function k defined by k(x)=the square root x-3
b.)The function F defined by F(x)=In(2x-1)
c.)The function f defined by f(x)=3 sin(2x)
d.)The function g defined by g(x)=4/x^2 - 4
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Simply find the set of all possible x-values, and the set of all possible y-values. For example,
 = \sqrt{x-3})
is not defined on real numbers if x < 3. Also, the range of k(x) is [0, infinity) because the square root of any real number is nonnegative.
Try the others the same way.
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