What does it mean when a function is negative for x

For example:

The function f(x) = x-1/(x-4)√x+2 is negative for x in

a) (1,4)
b) (-∞, 4)
c) (-∞, 1)
d) (4, ∞)

SOMEBODY PLEASE HELP I DON'T UNDERSTAND THIS PLEASE!!!!!!!! ASAP!!!!!!!!!!!

(x-1)/(x-4)√(x+2)

is negative when (x-1)/(x-4) is negative

√(x+2) is always positive if it is defined
x>-2
(x-1)/(x-4)<0
is the same
(x-1)*(x-4)<0

so 1
and x>-2

so finally
1 ANSWER
a) (1,4)

It means that if you plug any value for x from that range, then f(x) will always be negative.

Also, your function is not clear. Is it supposed to be f(x) = x -[1/(x-4) ] √x + 2, which is the same as f(x) = x - [ √x / (x-4) ] + 2 ? Is (x -2) completely under the square root sign, or just the x part?

Is the top of the fraction just 1, or (x -1) ? There's a big difference between x - 1 / (something ...) and (x-1) / (something ...).

a) if x=2, 2-1/(2-4)(sqrt(2)+2) is certainly negative
b and c can be ruled out because -/-=+ and d can
be ruled out because if x>4 f(x) will be positive