Question

what is the domain of the sqaure root of x^2-5x+4? So far I have x=1, 4, how do I use the inequality?

Answer 1

the domain will be greater than or equal to 1

Answer 2

what about the 4

Answer 3

\[x^{2}-5x+4 \ge 0\]
\[(x-4)(x-1) \ge 0\]
Now for the product to be positive, both factors must be positive or both must be negative
critical points are x=4,x=1
If x>4, then both will be positive
If x<1, then both will be negative
Therefore domain is, x>=4 or x<= 1
Interval notation
\[x \in (-\infty,1]\cup[4,\infty)\]