Question

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

Answer 1

`y=0.5(x-1)`

Explanation:

To find the inverse of a function, you have to substitute `y` for `x` in the equation and simplify to get a normal equation again. In this case, `f(x)` is `y`.

`y=2x+1`

`x=2y+1`

`2y+1=x`

`2y=x-1`

`y=0.5(x-1)`

So there you have it.

Answer 2

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

Explanation:

`f(x)=y`

`y=2x+1`

Switch the places of x and y:

`x=2y+1`

Now, solve for y so the function is once again written in terms of x:

`2y=x-1`

`y=(x-1)/2`

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

Where `f^(-1)(x)` denotes that the function is an inverse of the original function.