# Inverse functions

• Mar 23rd 2009, 05:12 AM
princess_21
Inverse functions
what is the inverse function of 3y=2x+7. How will I do that? thanks
• Mar 23rd 2009, 05:23 AM
chisigma
Any linear function of the type $\displaystyle y= a\cdot x + b$ , $\displaystyle a \ne 0$ has its inverse of the form $\displaystyle x= \frac {1}{a}\cdot (y-b)$. In your case is $\displaystyle a=\frac {2}{3}$ , $\displaystyle b= \frac{7}{3}$…

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Mar 23rd 2009, 05:30 AM
princess_21
Quote:

Originally Posted by chisigma
Any linear function of the type $\displaystyle y= a\cdot x + b$ , $\displaystyle a \ne 0$ has its inverse of the form $\displaystyle x= \frac {1}{a}\cdot (y-b)$. In your case is $\displaystyle a=\frac {2}{3}$ , $\displaystyle b= \frac{7}{3}$…

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

you mean that the inverse of y=f(x) is x=f(y)?? I will just make it in terms of x

in my question

$\displaystyle 3y=2x+7$

$\displaystyle 3y-7=2x$

$\displaystyle f(x)=\frac{3y-7}{2}$
• Mar 23rd 2009, 05:38 AM
chisigma
Quote:

Originally Posted by princess_21
you mean that the inverse of y=f(x) is x=f(y)??...

More exactly the inverse of $\displaystyle y=f(x)$ is $\displaystyle x=f^{-1} (y)$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Mar 23rd 2009, 05:41 AM
princess_21
[quote=chisigma;286895]More exactly the inverse of $\displaystyle y=f(x)$ is $\displaystyle x=f^{-1} (y)$

can you give an example? i cant understand. $\displaystyle x=f^{-1} (y)$
• Mar 23rd 2009, 06:23 AM
chisigma
Simple examples of couples of 'direct' and 'inverse' functions are...

$\displaystyle y=f(x)=x^{2} \rightarrow x=f^{-1} (y)= \sqrt {y}$

$\displaystyle y= f(x)= \sin x \rightarrow x=f^{-1} (y)= \sin ^{-1} y$

$\displaystyle y= f(x) = e^{x} \rightarrow x=f^{-1} (y)= \ln y$

In it important to take into account that the inverse function often it is not a single value function, just as in three examples I have given…

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$