Question

Find the inverse of f(x)=2x+1

Answer 1

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

Explanation:

The inverse function is the function which when plugged in to the original one yields the argument (x).

Knowing this we do the following, let h(x) be the inverse function of f:

`f(x)=2x+1 \ \ \ \ f(h(x)) = 2(h(x)) + 1 = x\\h(x) = (x-1)/(2)\\Now \ we \ verify \ if \ it \ yields \ x.\\f(h(x)) = f((x-1)/(2)) = 2((x-1)/(2)) + 1 = x -1 + 1 = x\\Thus \ h(x) \ is \ the \ inverse\ function \ of \ f`

Answer 2

y=0.5(x-1)

Explanation:

To find the inverse of a function, you have to substitute yfor 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.