SOLUTION: find the domain for the following: f(x) = sqrt (3x-4) g(x) = (-2x+1) / (1-3x)

Algebra ->  Functions -> SOLUTION: find the domain for the following: f(x) = sqrt (3x-4) g(x) = (-2x+1) / (1-3x)       Log On


   

Question 104958: find the domain for the following:
f(x) = sqrt (3x-4)
g(x) = (-2x+1) / (1-3x)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For the first function,
f%28x%29=sqrt%283x-4%29
the value inside the square root must always be greater than or equal to zero for the function to be defined.
3x-4%3E=0
3x%3E=4
x%3E=4%2F3 The domain for f%28x%29=sqrt%283x-4%29
For the second function,
g%28x%29+=+%28-2x%2B1%29+%2F+%281-3x%29
you need to avoid any values that make the denominator zero since division by zero is undefined.
1-3x=0
1=3x
x=1%2F3
In this case, all values are acceptable except x=1/3.
x%3C1%2F3 and x%3E1%2F3 is the domain for g%28x%29=+%28-2x%2B1%29+%2F+%281-3x%29