ok so I cannot comprehend the answer to this math problem
F(x) = sqrt of 6 + x - x^2
I had to find the domain of the function

x = 3 and x = -2

the answer was {x| -2 =< x =< 3}

I was able to to do everything such as factoring it and finding the values of the x's but I dont understand how to write it in this format with the inequalites. Can you guys help me?
x is greater than -2 and less than 3

domain is x. so if you graphed it it would be near then middle of the graph.
Love, RamonesRock
It comes from the fact that if x is lower than -2 or greater than 3, the bit in the square root is less than zero, which means you can't take the square root.

So x's domain is any real number between -2 and 3, ie -2 < x < 3

Hope that helped.
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How do you determine which inequality sign to use though? Basically why =<?
Quote by Nemesis75
How do you determine which inequality sign to use though? Basically why =<?

because it can equal -2 or 3, and all in between

if it was just < it couldnt equal -2 or 3
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Quote by alexi_laiho
because it can equal -2 or 3, and all in between

if it was just < it couldnt equal -2 or 3

and what about if you put it as - 2 >= x >= 3?
Quote by Nemesis75
and what about if you put it as - 2 >= x >= 3?

ok to explain that i'll split it up

if you have -2 >= x it means x is less than or equal to -2
and if you have x >= 3 it means x is greater than or equal to 3

it isn't possible for x to be less than -2, and greater than 3 at the same time

hope that helps
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i learn math in french so this is all so weird to me.