How do you find the domain of y=sqrt(x^2 - 6 x + 5)?

1 Answer
Jul 30, 2017

The domain is x in (-oo,1] uu [5,+oo)

Explanation:

y=sqrt(x^2-6x+5)

What is under the square root sign is >=0

Therefore,

x^2-6x+5>=0

We factorise the inequality

(x-1)(x-5)>=0

Let f(x)=(x-1)(x-5)

We build a sign chart

color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaaaa)1color(white)(aaaaaaaaa)5color(white)(aaaaaaa)+oo

color(white)(aaaa)x-1color(white)(aaaa)-color(white)(aaaa)0color(white)(aaa)+color(white)(aaa)0color(white)(aaaa)+

color(white)(aaaa)x-5color(white)(aaaa)-color(white)(aaaa)0color(white)(aaa)-color(white)(aaa)0color(white)(aaaa)+

color(white)(aaaa)f(x)color(white)(aaaaa)+color(white)(aaaa)0color(white)(aaa)-color(white)(aaa)0color(white)(aaaa)+

Therefore,

f(x)>=0, when x in (-oo,1] uu [5,+oo)

graph{sqrt(x^2-6x+5) [-10, 10, -5, 5]}