Question

Which function below is the inverse of f(x)=7x-1/2

Answer 1

`f(x) = 7x -(1)/(2)`

replace f(x) by y

`y=7x -(1)/(2)`

Now to find the inverse of the function replace x with y and y with x , i.e. interchange x and y

`x=7y -(1)/(2)`

Now we have to solve for y

So add
`(1)/(2)` to both sides

`x+(1)/(2) = 7y`

Now divide both sides by 7

`(x)/(7) +((1)/(2))/(7) = y`

`(x)/(7) +(1)/(14) = y`

or

`y=(x)/(7) +(1)/(14)`

or

`f^(-1)(x) =(x)/(7) +(1)/(14)`