Question

What is the inverse of the function f(x) = 2x + 1?

Answer 1

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

Explanation:

To find the inverse, you want to swap the inputs with the outputs, which is why you have the swapped domain and range between a function and its range.

So, given f(x)=2x+1, its inverse would give,

x=2y+1.

Solve for y,

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

Therefore,
`y^(-1) =(1)/(2) x-(1)/(2)`

Answer 2

`h(x)=(1)/(2)x -(1)/(2) .`

Explanation:

if the initial function is f(x)=2x+1, then

x=2*h(x)+1;

2h(x)=x-1;

`h(x)=(x)/(2) -(1)/(2).`

PS. change design according the local requirements.