SOLUTION: The function f(x)=(x-1)/((x-4)sqrt(x+2)) is negative for x in a. (1,4) b. (4, infinite) c. (-infinite, 4) d. (-infinite, 1) Please tell me how to find the correct

Question 764030: The function
f(x)=(x-1)/((x-4)sqrt(x+2))
is negative for x in
a. (1,4)
b. (4, infinite)
c. (-infinite, 4)
d. (-infinite, 1)
Please tell me how to find the correct answer,
Thanks!
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The function
f(x)=(x-1)/((x-4)sqrt(x+2))
is negative for x in
a. (1,4)
b. (4, infinite)
c. (-infinite, 4)
d. (-infinite, 1)
----
x cannot be 1, 4, < -2
------
Draw a number line and plot -2,1,and 4.
---
Find the intervals on the line where f(x) is negative.
Test x = 0 ; you get -/(-*+) = + so no solutions in the interval (-2,1)
Test x = 2 ; you get +/(-*+) = - for interval (1,4)
Test x = 10 ; you get +/(+*+) = + so no solutions in (4,+oo)
==============
Ans: b
===============
Cheers,
Stan H.
===============

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The function
f(x)=(x-1)/((x-4)sqrt(x+2))
is negative for x in:
***
make a chart:
...TP......(x-1).....(x-4)......(x+2......f(x).
.. -2.......-............-............0..........+
....1........0............-............+..........-
....3........+............-............+..........-
.. .4........+...........0............+..........+
. >5.......+...........+.............+.........+
f(x) is negative: [1,4)
Notes:
TP: test point
x≥-2 because of (x+2) radican

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