Question

Inverse of f(x)?

f(x)=`(alpha)/(alphax-1)`

Answer 1

`f^-1(x)=(alpha+x)/(xalpha)`

Explanation:

We have: `f(x)=alpha/(alphax-1)`

Now, `f(f^-1(x))=x` This means that when we plug our inverse function to our function, it equals `x`.

We can say that:
`x=alpha/(alpha*f^-1(x)-1)`

=>`x(alpha*f^-1(x)-1)=alpha`

=>`xalpha*f^-1(x)-x=alpha`

=>`xalpha*f^-1(x)=alpha+x`

=>`f^-1(x)=(alpha+x)/(xalpha)`