1. ## 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

2. 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 $\quad \Rightarrow \quad x= \frac{(y-b)}{a}$
$or\ x=\frac{1}{a}y-\frac{b}{a}$
$\therefore f^{-1} (y)=\frac{1}{a}y-\frac{b}{a} \quad \Rightarrow \quad (\because f(x)=y , taking inverse both side )$
$or\ \color {blue} f^{-1} (x)=\frac{1}{a}x-\frac{b}{a}$................(1)
but given $f^{-1}(x)=8x-3$................(2)
on comparison eq(1) and (2)
$\frac{1}{a}=8 \quad \Rightarrow a= \frac{1}{8}$
and
$\frac{b}{a}=3 \quad \Rightarrow b=3a={3\over 8}$

3. Thank you very much!

4. 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".

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