find the domain of the function: g(x)=2/5-9x
To find the domain of a function, we need to determine the set of all possible values for the independent variable (in this case, x) that would not result in an undefined or imaginary output.
In this specific function, g(x) = 2/(5 - 9x), the denominator 5 - 9x cannot be equal to zero because division by zero is undefined. Therefore, to find the domain, we need to solve the equation 5 - 9x = 0.
First, let's isolate x by moving 5 to the other side:
5 - 9x = 0
-9x = -5
Next, divide both sides by -9 to solve for x:
x = -5/-9
Simplifying the right side gives x = 5/9.
Therefore, the only value that would make the denominator equal to zero is x = 5/9. Thus, the domain of the function g(x) = 2/(5 - 9x) would be all real numbers except x = 5/9.