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

1 Answer
Apr 15, 2018

Answer:

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

Explanation:

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}#.