F(x)=1/(x^2-5): find largest A so f(x) defined on [-10,A]

jemadd2

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Suppose F(x)=1/(x^2-5). What is the largest value of A such that f(x) is defined on the interval [-10,A)?

I can't believe I don't know how to do this =/
 
jemadd2 said:
Suppose F(x)=1/(x^2-5). What is the largest value of A such that f(x) is defined on the interval [-10,A)?

What is the range of the given function F(x)?

Please share with us your work, indicating exactly where you are stuck - so that we know where to begin to help you.
 
jemadd2 said:
Suppose F(x)=1/(x^2-5). What is the largest value of A such that f(x) is defined on the interval [-10,A)?
Can you divide by zero?

What is the first (leftmost) x-value which would cause division by zero?

:wink:
 
If I am interpreting correctly, F(x)=1x25\displaystyle F(x)=\frac{1}{x^{2}-5}

Then, F(x)=f(x)=2x(x25)2\displaystyle F'(x)=f(x)=\frac{-2x}{(x^{2}-5)^{2}}

Now, what results in division by 0?. That's a start.
 
Domain of f(x):(,5)(5,5)(5,)\displaystyle f(x): (-\infty,-\sqrt{5})\cup(-\sqrt{5},\sqrt{5})\cup(\sqrt{5},\infty). Can you take it from here?

Perhaps I should have said the range of f(x): (,.2](0,)\displaystyle f(x): \ (-\infty,-.2]\cup(0,\infty)
 
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