Help with an Inverse Equation

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November 18th 2011, 09:22 AM
rpgnick85

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
November 18th 2011, 10:04 AM
skeeter

Re: Help with an Inverse Equation

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

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

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

$7xy+3x = 2y$

$3x = 2y - 7xy$

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

$y = g^{-1}(x) = \frac{3x}{2-7x}$
November 18th 2011, 10:32 AM
rpgnick85

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!
November 18th 2011, 11:45 AM
skeeter

Re: Help with an Inverse Equation

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

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

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

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