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Calculus/Please assist with question 2.7

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Question
I've attached the question and a link... I've done all of it but I am just stuck with question 2.7! I would really appreciate the assistance...

http://rs1287.pbsrc.com/albums/a626/Chantell_Young/Mobile%20Uploads/utf-8BcXVlc3

Answer
Hi Chantell,
The inequality f(x).g(x) >= 0 is satisfied by all the set of points for which:
f(x) > 0 and g(x) > 0
together with those for
f(x) < 0 and g(x) < 0
and whenever
f(x) = 0 or g(x) = 0
It simply means that the inequality is satisfied when both functions have positive values or both have negative values or when any of them is zero.
As can be seen;
for x < -3, f(x) < 0 and g(x) < 0
for -3 < x < 1, f(x) > 0 and g(x) > 0
at x = -3, f(x) = g(x) = 0
at x = 1, f(x) = 0
and the complete solution to the inequality is x ≤ 1

You can also easily check to see that for x > 1, f(x) < 0 and g(x) > 0 which makes the product f(x).g(x) < 0 and doesn't satisfy the inequality.

Regards

Calculus

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