How do you find the domain of the function: #g(x)=3/(10-3x)#?

Question

Hazel Anglin · Accepted Answer

The domain of #g(x) = 3/(10 - 3x# is #x != 10/3#.

THe domain of any function is the set of all the values which can be used for the input variable, which is #x#. The domain is All Real Numbers unless tere is an #x# in a denominator of a fraction or in a radicand of a root with an even index. If there is an #x# in a denominator, to determine the restrictions on the domain, set the expression from the denominator equal to #0# and solve for #x#. The solution(s) obtained willl be the values which cannot be included in the domain. If there is an #x# in a radicand of a root with an even index, set the expression from the radicand less than #0# and solve for #x#. The solution range obtained cannot be included in the domain. This is how to find the domain for this function: #g(x) = 3/(10 - 3x)# #10 - 3x = 0# #10 - 10 - 3x = 0 - 10# #-3x = -10# #(-3x)/3 = (-10)/-3# #x = 10/3# The domain of the function is #x != 10/3#. In set-builder notation, this is written #D = {x|x != 10/3}#.

Avery Alexander · Answer

undefined To find the domain of the function g(x) = 3/(10 - 3x), you need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined. So, set the denominator equal to zero and solve for x. In this case, the denominator is 10 - 3x, so you set 10 - 3x = 0 and solve for x. After solving for x, you'll have the domain of the function.