Question

given f(x) = √((x-1)(x-3))
what is the domain of f ?

Answer 1

x-intercept: (1,0),(3,0)
y-intercept (0,√3)

Answer 2

\[\sqrt{(x - 1)(x - 3)}\]

determine when this function is negative. the function is negative whenever

(x -1)(x - 3) is negative

this occurs whenever (x - 1) and (x - 3) have opposite signs

Answer 3

so the only restriction on the domain is the interval (1, 3) where the two factors have opposite signs.

Answer 4

thank you!