Algebra Domain

[joannamartinez]

I need help with this problem please. I need to find the domain of the fraction g(x)= 6/9-5x. I know it is a real number but I cannot get the exact real number. I come with with different ones, like x >=9/5 or x is not equal to 0 or x is not equal to 9/5 or x is not equal to 6. Which is correct please? Thank you for your help.

 

[BigGlenntheHeavy]

\(\displaystyle Is \ that \ g(x) \ = \ \frac{6}{9}-5x \ or \ g(x) \ = \ \frac{6}{9-5x}?\)

 

[joannamartinez]

The second one is correct. Thank you.

 

[BigGlenntheHeavy]

\(\displaystyle The \ domain \ is \ the \ set \ of \ all \ reals \ except \ x \ = \ \frac{9}{5}, \ Why?\)

 

[joannamartinez]

Is it becuase the fraction is improper? I am really not too sure why. So, would the answer be x>=9/5 or would it be x is not equal to 9/5? These are confusing. I think it is x is not equal to 9/5. Is that correct? Thank you.

 

[BigGlenntheHeavy]

\(\displaystyle g\bigg(\frac{9}{5}\bigg) \ = \ \frac{6}{0}, \ does \ that \ tell \ you \ anything?\)

\(\displaystyle The \ domain \ of \ g(x) \ is \ (-\infty,9/5)U(9/5,\infty)\)

 

[joannamartinez]

Yes, it does. It tells me that I am way off! Thank you for simplifying it for me. I appreciate your patience and help.