Question

Find the inverse: f(x)=x+5/3x-1

f^-1x=

Answer 1

f-1(x) = (x + 5)/(3x - 1).

Explanation:

Let y = (x + 5)/ (3x - 1)

3xy - y = x + 5

3xy - x = y + 5

x(3y - 1) = y + 5

x = (y + 5)/(3y - 1)

So f-1(x) = (x + 5)/(3x - 1).

Answer 2

We have
`f(x)=(x+5)/(3x-1)`.

To find inverse function
`f^(-1)(x)` we substitute x with
`f^(-1)(x)` and vice-versa to get

`x=(f^(-1)(x)+5)/(3f^(-1)(x)-1)`

Now solve for
`f^(-1)(x)`. Note that I will use
`j` instead.

`</p><p>x=(j+5)/(3j-1) \\</p><p>x(3j-1)=j+5 \\</p><p>3jx-x=j+5 \\</p><p>3jx-x-j-5=0 \\</p><p>3jx-j=x+5 \\</p><p>j(3x-1)=x+5 \\</p><p>j=(x+5)/(3x-1)</p><p>`

So we find that
`f(x)=f^(-1)`.

Hope this helps.