How do you find the domain and range of #f(x)=x#?

Question

Nathan Axel · Accepted Answer

The domain of #f(x) = x# is the whole of the real numbers #RR#. The range is also the whole of #RR#.

As stated: #f(x) = x# The domain of #f(x)# is the set of values for which #f(x)# is defined. In the context of Algebra I that means a subset of the real numbers #RR#. In the case of the given #f(x)#, it is well defined for any #x in RR#, so the domain is the whole of #RR#, i.e. #(-oo, oo)# The range of #f(x)# is the set of values that it can take for some value of #x#. Given any real number #y#, let #x = y#. Then #f(x) = x = y#. So the range of #f(x)# is the whole of #RR# too. The graph of #f(x) = x# is a diagonal line like this: # graph{x [-10, 10, -5, 5]} For every #x# coordinate there is a corresponding point on the line. That tells us that the domain of #f(x)# is the whole of #RR#. For every #y# coordinate there is a corresponding point on the line. That tells us that the range of #f(x)# is the whole of #RR#.

Eli Assouline · Answer

undefined To find the domain and range of the function $ f(x) = x $:

**Domain:**
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
For the function $ f(x) = x $, the domain is all real numbers since there are no restrictions on the input values.

**Range:**
The range of a function is the set of all possible output values (y-values) that the function can produce.
For the function $ f(x) = x $, the range is also all real numbers because for every input value of x, there is a corresponding output value, which can be any real number. Therefore, the range is the same as the domain, which is all real numbers.