# Math Help - [SOLVED] Verifying Inverse of this Function

1. ## [SOLVED] Verifying Inverse of this Function

$g(x)=\frac{2x-1}{x+3}$

My Attempt At The Inverse

Let $g(x)=z$

$(x+3)(z)=2x-1$

$xz+3z=2x-1$

$1+3z=2x-xz$

$1+3z=x(2-z)$

$\frac{1+3z}{2-z}=x$

$g^-1(x)=\frac{1+3x}{2-x}$

Where did I make a mistake?

Thanks!

2. Originally Posted by unstopabl3
$g(x)=\frac{2x-1}{x+3}$

My Attempt At The Inverse

Let $g(x)=z$

$(x+3)(z)=2x-1$

$xz+3z=2x-1$

$1+3z=2x-xz$

$1+3z=x(2-z)$

$\frac{1+3z}{2-z}=x$

$g^-1(x)=\frac{1+3x}{2-x}$

Where did I make a mistake?

Thanks!
Why do you think there's a mistake. There is no mistake.

3. Okay, great then!

Thanks for the verification!