You are here:

# Calculus/Please assist with question 2.7

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...

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
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you sooooo much for taking your time to assist me, I really appreciate it! Many thanks :) Regards Chantell

• Ask a Question

Calculus

Volunteer

#### Ahmed Salami

##### Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I believe i would be very helpful in calculus and can as well help a good deal in Physics with most emphasis directed towards mechanics.

##### Experience

Aspiring theoretical physicist. I have been doing maths and physics all my life.

Education/Credentials
I teach mathematics and engineering physics.