Question

How do you find the equation for the inverse of `y=2x+1`?

Answer 1

The inverse is `=(x-1)/2`

Explanation:

Our equation is

`y=2x+1`, we have `y` as a function of `x`

We need `x` as a function of `y`

`2x=y-1`

`x=(y-1)/2`

Therefore. the inverse is

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

Verification

`[yoy^-1](x)=y((x-1)/2)=2*(x-1)/2+1=x`

The inverse of `y` is the image of `y` in the line `y=x`

graph{(y-x)(y-2x-1)(y-x/2+1/2)=0 [-6.24, 6.244, -3.12, 3.12]}

Answer 2

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

Explanation:

`"rearrange making x the subject"`

`2x+1=y`

`rArr2x=y-1`

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

`"expressing the inverse function in terms of x gives"`

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