Can someone please find the domain of this problem?

Question

I'm not trying to slack or anything and make people do my work, I just have such a hard time with finding the domain.

The problem is this:

sqrt of (x-1)/(x-4) then outside of the fraction is +18

Thanks!

Answer 1

When finding the domain of a function you start by assuming it is the entire set of real numbers then exclude any number which causes

a. A denominator to equal zero

b.  An expression under a square root or even root radical

to become negative

so if the function is  y=f(x)=√[(x-1)]/(x-4)+18

and I assume the only part under the square root radical is

x-1

then we know the domain must satisfy

x≥1  to keep negatives out from under the square root

and x is not equal to 4 to keep the denominator from

equaling zero.  

That means the domain is all x greater than or equal to one

EXCEPT x=4 .

We would write this, using interval notation as

domain of f(x) is [1,4)U(4,∞)

Answer 2

If it is sqrt (x-1)  / (x-4) , then

x must be above 1 and cannot equal 4

[1,4) U (4,infinity)

If it is sqrt [(x-1) / (x-4)] , then

x cannot equal 4

x can be less than or equal to 1

x can be greater than 4

(-infinity,1] U (4, infinity)