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

2 Answers
Narad T.
Aug 8, 2017

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]}

Jim G.
Aug 8, 2017

#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)#

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