f(x)=x-1 and g(x)=2x
Perform the indicated and state the domain
f(x)/g(x)
If 2x is in the denominator, then x cannot be equal to zero, so that is excluded from the domain.
To find the expression f(x)/g(x), we need to divide f(x) by g(x).
First, let's substitute the given functions into the expression f(x)/g(x):
f(x)/g(x) = (x-1)/(2x)
Next, we can simplify the expression by canceling out common factors in the numerator and denominator:
f(x)/g(x) = (x-1)/(2x) = (x-1)/(2*x) = (x-1)/(2x/1) = (x-1)*(1/2)*(1/x) = (x-1)/2x
So, the simplified expression is (x-1)/2x.
Now let's determine the domain of this expression. Since x is in the denominator, we need to consider any values that would make the denominator equal to zero. In this case, the denominator is 2x, so we need to find the value(s) of x that make 2x equal to zero.
Since 2x = 0 implies x = 0, the value x = 0 is excluded from the domain.
Therefore, the domain of the expression f(x)/g(x) is all real numbers except for x = 0.