# Inverse funciton

• Oct 27th 2009, 09:12 AM
Oasis1993
Inverse funciton
The function f(x)= ax+b , f-1(x)=8x-3. Find a and b

I would be very happy if you explained how to do it.

Thank you
• Oct 27th 2009, 09:25 AM
ramiee2010
Quote:

Originally Posted by Oasis1993
The function f(x)= ax+b , f-1(x)=8x-3. Find a and b

I would be very happy if you explained how to do it.

Thank you

let f(x)= ax+b =y (say)
then ax+b =y $\displaystyle \quad \Rightarrow \quad x= \frac{(y-b)}{a}$
$\displaystyle or\ x=\frac{1}{a}y-\frac{b}{a}$
$\displaystyle \therefore f^{-1} (y)=\frac{1}{a}y-\frac{b}{a} \quad \Rightarrow \quad (\because f(x)=y , taking inverse both side )$
$\displaystyle or\ \color {blue} f^{-1} (x)=\frac{1}{a}x-\frac{b}{a}$................(1)
but given $\displaystyle f^{-1}(x)=8x-3$................(2)
on comparison eq(1) and (2)
$\displaystyle \frac{1}{a}=8 \quad \Rightarrow a= \frac{1}{8}$
and
$\displaystyle \frac{b}{a}=3 \quad \Rightarrow b=3a={3\over 8}$
• Oct 27th 2009, 11:30 AM
Oasis1993
Thank you very much!
• Oct 28th 2009, 07:52 AM
HallsofIvy
Just to put in my oar: 8x- 3 says "first multiply x by 8 and then subtract 3".

The "inverse" is the inverse of the original operarations ("divide by 8" rather than "multiply by 8" and "add 3" rather than "subtract 3") done in the opposite order.

So the inverse of "first multiply x by 8 and then subtract 3" is "first add 3 to x and then divide by 8".

$\displaystyle f(x)= \frac{x+ 3}{8}= \frac{1}{8}x+ \frac{3}{8}$