Domain of F(X) = log7 (100 - x^2), where 7 is the base

[jenjen]

I'm wondering if I solved this problem correctly

Find the domain
F(X)=log7 (100-x^2)
7 is the base

F(x)=-x^2+100>0
F(x)=-x^2>-100 divide by -x^2
F(x)=x+10 and x-10

sorry i dont know the sign for infinty

negative infinty, 10 U -10, positive infinty

Thanks!!

 

[royhaas]

Re: Domain of a LOG

Check again. You must have \(\displaystyle 100 > x^2\), since the domain of a logarithm must be strictly positive.

 

[jenjen]

Re: Domain of a LOG

does that mean it would only be negative infinty postive 10

 

[Mrspi]

Re: Domain of a LOG

I'm wondering if I solved this problem correctly

Find the domain
F(X)=log7 (100-x^2)
7 is the base

F(x)=-x^2+100>0
F(x)=-x^2>-100 divide by -x^2
F(x)=x+10 and x-10

sorry i dont know the sign for infinty

negative infinty, 10 U -10, positive infinty

Thanks!!

You can't find a log of zero or a negative number, so 100 - x^2 must be positive, or...

100 - x^2 > 0
(10 - x)(10 + x) > 0

The "critical values" for x are 10 and -10, because those values of x will make the product EQUAL to 0.

The critical values divide the set of real numbers into three subregions: (-infinity, -10), (-10, 10), and (10, infinity)

Check each region to see where 100 - x^2 > 0. That will be the domain for the function.

 

[jenjen]

Re: Domain of a LOG

thanks