Find the domain of the following functions:

A. F(x)=root x-1
B.f(x)=1/(x squ-4)
C.F(x)= root 4-x squ
D.f(x)=|x-1|

A. sqrt(x-1) is basically sqrt(x) transformed 1 unit to the right, Hence domain is [1,positive infinity)

B. 1/(x^2-4) is undefined when denominator = 0.
x^2-4=0
x^2 = 4
x = -2 or 2

Hence, domain is R\{-2,2}. This denotes all real numbers except -2 and 2.

C.sqrt(4-x^2) is only defined if 4-x^2 is greater or equal (>=) to 0. So to find where it's not defined simply solve this inequality:
4-x^2<0
x^2>4
So, x = -2 or 2

Now do some substitution to test it.
if x = -3 or 3
sqrt(4-x^2) will be undefined as you can't take a squareroot of negative number. So domain is [-2,-2]

D. This is basically |x| shifted 1 unit to the right but this graph is still continuous all the way, So domain is R (denotes all real numbers)

√(x-1)
x-1 ≥ 0
x≥ 1, D
1/(x²-4)
x²-4 must Not =0
or x² not = 4
or x not = ± 2
D= all real numbers but ±2
C is similar to A
D all real numbers, x can be any number.