# Two Equations (solving for inverses)

• Jan 28th 2010, 09:50 AM
TaylorM0192
Two Equations (solving for inverses)
Find the inverse equations of the following:

1. $\displaystyle f(x) = 3x + ln(x)$

2. $\displaystyle g(x) = \frac{x+1}{2x+1}$

So the equations become...

1. $\displaystyle x = 3y + ln(y)$

2. $\displaystyle x = \frac{y + 1}{2y + 1}$

Sovle for $\displaystyle y$.

I've played with the algebra a few different ways, especially on the rational function, but I still can't solve for 'y' in either equation! :( I've also graphed both functions, and they both appear to have an inverse (geometrically anyway).

Step-by-step algebra would be helpful - thanks!
• Jan 28th 2010, 10:41 AM
[quote=TaylorM0192;446936]Find the inverse equations of the following:

1. $\displaystyle f(x) = 3x + ln(x)$

2. $\displaystyle g(x) = \frac{x+1}{2x+1}$

___________________________________________

2.

$\displaystyle g^{-1}(x) = \frac{1-x}{2 x-1}$
• Jan 28th 2010, 10:45 AM
TaylorM0192
Quote:

Originally Posted by TaylorM0192
Find the inverse equations of the following:

1. $\displaystyle f(x) = 3x + ln(x)$

2. $\displaystyle g(x) = \frac{x+1}{2x+1}$

___________________________________________

1.

$\displaystyle f^{-1}(x) = 1/3 W(3 e^x)$

2.

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

Your $\displaystyle g^{-1}(x)=\frac{1-x}{2x-1}$ cannot be the inverse of my $\displaystyle g(x)=\frac{x+1}{2x+1}$ (confirmed by the graphs of each & algebraically by $\displaystyle g(g^-1(x))$ not being equal to 'x').

I don't know what $\displaystyle f^{-1}(x) = 1/3 W(3 e^x)$ is...
• Jan 28th 2010, 12:47 PM
TaylorM0192
Figured out $\displaystyle g^-1(x) = \frac{x-1}{1-2x}$.

Still don't know $\displaystyle f^-1(x)$ though. :(
• Jan 28th 2010, 12:56 PM
Figured out $\displaystyle g^-1(x) = \frac{x-1}{1-2x}$.
Still don't know $\displaystyle f^-1(x)$ though. :(
$\displaystyle f^{-1}(x) = \frac {1}{3} W(3 e^x)$