Help with an Inverse Equation

I am really stumped on this homework question and I am trying to better understand how to find the inverse, domain, and range.

The equation g(x) = -2x/(-7x-3). I feel like I am not going about getting the inverse the right way to begin with.

Thank you

-Rick

Re: Help with an Inverse Equation

$\displaystyle g(x) = y = \frac{2x}{7x+3}$

$\displaystyle x = \frac{2y}{7y+3}$

$\displaystyle x(7y+3) = 2y$

$\displaystyle 7xy+3x = 2y$

$\displaystyle 3x = 2y - 7xy$

$\displaystyle 3x = y(2 - 7x)$

$\displaystyle y = g^{-1}(x) = \frac{3x}{2-7x}$

Re: Help with an Inverse Equation

Thank you very much for the help - I was multiplying wrong on one side. As far as interval notation for the domain and range goes how would I indicate both with the parenthesis, brackets and U? I believe the domain to not include 2/7 but I am unsure how to find the range once I graph it and to correctly notate both.

Thanks again!

Re: Help with an Inverse Equation

for $\displaystyle g(x)$ , $\displaystyle 7x+3 \ne 0$ ...

domain: $\displaystyle \left(-\infty, -\frac{3}{7} \right) \cup \left(-\frac{3}{7} , \infty \right)$

the range of $\displaystyle g(x)$ is the domain of $\displaystyle g^{-1}(x)$