Question

Find the inverse of f(x)= (5x - 1) / 6

Answer 1

`f^(-1)(x)\text{ = }\frac{6x\text{ + 1}}{5}`

Step-by-step explanation

We want to find the inverse:

`f(x\text{) = }\frac{5x\text{ - 1}}{6}`

First, change f(x) to y:

`y\text{ = }\frac{5x\text{ - 1}}{6}`

Now, make x the subject of formula:

`\begin{gathered} 6y\text{ = 5x - 1} \\ 6y\text{ + 1 = 5x} \\ x\text{ = }\frac{6y\text{ + 1}}{5} \end{gathered}`

Now, change x to f-1(x), change y to x:

`f^(-1)(x)\text{ = }\frac{6x\text{ + 1}}{5}`

That is the inverse.