Question

Use integers or fractions for any numbers in the expression.

Answer 1

Consider the following injective function:

`f(x)=(3x+6)/(x-5)`

this is equivalent to:

`y=(3x+6)/(x-5)`

by cross-multiplication, this is equivalent to:

`(x-5)y\text{ = 3x+6}`

now, applying the distributive law, we get:

`xy-5y\text{ = 3x+6}`

this is equivalent to:

`xy\text{ -5y -3x = 6}`

Applying the common factor, we get:

`x(y-3)\text{ -5y = 6}`

this is equivalent to:

`x\text{ (y-3)}=\text{ 6+5y}`

solving for x, we get:

`x\text{ = }(6+5y)/(y-3)`

so that, we can conclude that the correct answer is:

`f^(-1)(x)=(6+5x)/(x-3)`