Question

What is the inverse of the function

Answer 1

`\huge\boxed{h(x) = (1)/(2) x - (1)/(2)}`

Explanation:

`f(x) = 2x+1`

Put f(x) = y

`y = 2x + 1`

Interchange x and y

`x = 2y+1`

Solve for y

`x = 2y+1`

Subtracting 1 to both sides

`x-1 = 2y`

Dividing both sides by 2

`(x-1)/(2) = y \\\\ OR\\\\ y = (x-1)/(2)`

Put y = h(x)

`\bold{h(x) = (1)/(2) x - (1)/(2)}`

Answer 2

1/2x -1/2

Explanation:

f(x) = 2x+1

y = 2x+1

Switch x and y

x = 2y+1

Solve for y

Subtract 1

x-1 = 2y+1-1

x-1 =2y

Divide by 2

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

1/2x -1/2 = y

The inverse is 1/2x -1/2