Question

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

Answer 1

We have $f(x)=\dfrac{x+5}{3x-1}$.

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

$x=\dfrac{f^{-1}(x)+5}{3f^{-1}(x)-1}$

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

$x=\dfrac{j+5}{3j-1} \\x(3j-1)=j+5 \\3jx-x=j+5 \\3jx-x-j-5=0 \\3jx-j=x+5 \\j(3x-1)=x+5 \\j=\dfrac{x+5}{3x-1}$

So we find that $f(x)=f^{-1}$.

Hope this helps.

Answer 2

Answer:

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

Step-by-step 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).