Question

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

Answer 1

Answer:

$h(x)=\frac{1}{2}x -\frac{1}{2} .$

Step-by-step explanation:

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

x=2*h(x)+1;

2h(x)=x-1;

$h(x)=\frac{x}{2} -\frac{1}{2}.$

PS. change design according the local requirements.

Answer 2

Answer:

$y^{-1} =\frac{1}{2} x-\frac{1}{2}$

Step-by-step 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=$\frac{1}{2} x-\frac{1}{2}$

Therefore, $y^{-1} =\frac{1}{2} x-\frac{1}{2}$