Question

How do I solve and what would the answer be?

Answer 1

We have the next given function:

`f(x)=(2)/(x-5)`

First, replace f(x) = y:

`y=(2)/(x-5)`

Then, interchange x and y:

`x=(2)/(y-5)`

Now, solve the equation for y:

- Multiply both sides by (y-5)

`x(y-5)=(y-5)(2)/(y-5)`
`x(y-5)=2`

- Divide both sides by x:

`(x(y-5))/(x)=(2)/(x)`
`y-5=(2)/(x)`

Finally, add both sides 5:

`y-5+5=(2)/(x)+5`

Hence, the inverse function for f(x) is given by:

`y=(2)/(x)+5`