how do i find the inverse of f(x)=9/11x

Question

aum · Answer

$$
f(x) = \frac{9}{11}x ~~ \text{ OR } ~~ f(x) = \frac{9}{11x}
$$

aum · Answer

Which one of the above is the correct problem?

anonymous · Answer

the second one

anonymous · Answer

h

aum · Answer

y = 9 / (11x)
solve for x:
multiply both sides by 1x
y * x = 9/11
divide both sides by y:
x = 9 / (11y)
interchange x and y:
y = 9/(11x)
Inverse = 9/(11x)

anonymous · Answer

i dont get it...

aum · Answer

If you are given a function f(x) and asked to find the inverse, these are the steps:
1. Replace f(x) by y.   Here we rewrote f(x)=9/(11x)  as  y = 9/(11x)
2. Solve for x.  Here, x = 9/(11y)
3. Interchange x and y.  y = 9/(11x)
4. Replace y with $f^{-1}(x)$.  Therefore the inverse function is: $\large f^{-1}(x) = \frac{9}{11x}$.

aum · Answer

Here the inverse function is same as the original function.
This happens whenever the function is symmetrical about the y = x line.

anonymous · Answer

alright, its just that i have to write the question like this:

aum · Answer

???

anonymous · Answer

f^-1(x) = ax +b/ cx + d)

aum · Answer

$$
\large f^{-1}(x) = \frac{9}{11x} = \frac{0x + 9}{11x + 0}
$$a = 0, b = 9, c = 11, d = 0