What does it mean when a function is negative for x?

Question

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!!!!!!!!!

Answer 1

it means "y" or f(x) is negative, the function is below the x-axis.



look at something simple:

y = f(x) = x^2 - 4

y is negative for x when x is between -2 and 2, otherwise it's positive.



unfortunately, the way you've written the function, I'm not sure what's in the numerator or the denominator. Is it (x-1) in the numerator or just 1(as written). And is the denominator both (x-4) and √x+2 --- or is that just √x, then add 2. nope -- too many options the way it is written.



BUT, you can figure this out by putting a value for x from each interval and seeing what makes the function negative.



that's it! ;)