G(x)=x/x^2-5x

Question

Find the domain of the function 

Answer 1

Set your denominator equal to zero and solve for x. You do this because in math, dividing by 0 is a no-no and you want to find what x values would make your denominator 0.

 

x^2 -5x = 0

 

Both terms have 'x' in common, so factor it out.

 

x (x-5) =0 

 

Set each term equal to zero and solve; those values you exclude from your domain. 

 

Write answer in the notation your teacher asks for: whether interval notation or a sentence like 'all real values except...'

 

Hope this helps.

Answer 2

You can't have 0 as your denominator; therefor

 

   X^2 - 5X can't = 0

 

factor

 

   X ( X - 5) does not = 0

 

Domain does not equal 0 or 5

Answer 3

I assume you mean

 

G(x) = x / (x² - 5x)

 

Factor out x from the denominator and get

 

G(x) = x / [x(x-5)]

 

Note an x cancels out in both the numerator and denominator.

 

G(x) = 1 / (x - 5)

 

The domain is all real numbers except x = 5.