Find the domain of the function
h(x) = (x/ x-1)
I need to know how to solve this, not just the answer! Help!
sorry correct functin is H(x) = log_3 (x/ x-1)
We know that log is undefined for x<=0.
So, x/(x-1) > 0
We also know that x/x-1 is not defined for x=1
so, except for x=1,
x > 0 and x-1 > 0 means x > 1
or
x<0 and x-1 < 0 meaning x < 0
So, the domain is x<0 or x>1
Thank you Steve
To find the domain of a function, you need to determine the set of values for the independent variable (x) for which the function is defined.
In this case, we are given the function:
h(x) = x / (x - 1)
To find the domain, we need to identify any values of x that would make the function undefined.
In general, a fraction is undefined when the denominator is equal to zero. So, to find the values of x that make the function undefined, we set the denominator equal to zero and solve for x:
x - 1 = 0
Adding 1 to both sides, we get:
x = 1
Therefore, the function h(x) is undefined for x = 1 since it results in a division by zero.
Hence, the domain of the function h(x) = x / (x - 1) is all real numbers except x = 1.