Question

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

Answer 1

`(x - 1) / 2`

Answer 2

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

Explanation:

Given: f(x)=2x+1

To find: The inverse of f(x)

Step 1: Set f(x)=y

y = 2x + 1

Step 2: Switch x and y

x = 2y + 1

Step 3: Solve for y

2y=x-1

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

We assumed y=f(x)

switch x and y

Thus,
`f^(-1)x=y`

Hence, The inverse of f(x)=2x+1 is
`f^(-1)(x)=(x-1)/(2)`