Question

Please view the picture for the problem.

Answer 1

Notice that we have common denominator 2, so we can split the denominator to express the function in the form
`f(x)=mx+b`
where

`m` is the slope

`b` is the y-intercept


`f(x)= (3x-1)/(2)`

`f(x)= (3)/(2) x- (1)/(2)`
Look what we have here, a linear function! We know that the domain and range of linear functions is the real numbers.
We can conclude that:
the domain of the function is all the real numbers
the range of the function is all the real numbers

Now, to find the inverse of our function, we are going to replace
`f(x)` with
`y`; then, we are going to interchange
`x` and
`y` and solve for
`y`:

`f(x)= (3)/(2) x- (1)/(2)`

`y= (3)/(2) x- (1)/(2)`

`x=(3)/(2) y- (1)/(2)`

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

`3y=2x+1`

`y= (2)/(3) x+ (1)/(3)`

`f^(-1)(x)=(2)/(3) x+ (1)/(3)`
The inverse of our linear function, is another linear function, so we can conclude that:
the domain of the inverse function is all the real numbers
the range of the inverse function is all the real numbers