Find the domain of
`f(x) = sqrt(x^(2) - 25x + 144)`

Explanation

For f(x) to be defined, expression under square root `ge 0` i.e., `x^(2) - 25x + 144 ge 0`
when `x^(2) - 25 x + 144 = 0`
`(x - 9) (x-16) = 0`
`rArr` Either x -9 = 0 or x - 16 = 0
`:.` x = 9, 16
Sign scheme for `x^(2) - 25 x + 144` is as follows

Take a point on the number line in any sub-interval and find the value of the expression at that point.
Here, suppose x = 0 ltbr. f(0) `= 144 gt 0`
Since none of the roots of `x^(2) - 25x +144 = 0` is repeated, the sign of the expression changes alternately in adjacent subintervals.
Hence `x le 9` or `x ge 46`
`:.` Domain of `f(x) = ]-oo, 9] cup [16, oo[`