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

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

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Answer 1 · 2017-08-08T09:03:04

The inverse is $= \frac{x - 1}{2}$ $=(x-1)/2$

Explanation:

Our equation is

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

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

$2 x = y - 1$ $2x=y-1$

$x = \frac{y - 1}{2}$ $x=(y-1)/2$

Therefore. the inverse is

$y^{- 1} = \frac{x - 1}{2}$ $y^-1=(x-1)/2$

Verification

#yoy^-1=y((x-1)/2)=2*(x-1)/2+1=x#

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

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

Answer 2 · 2017-08-08T10:33:40

$f^{- 1} (x) = \frac{1}{2} (x - 1)$ $f^-1(x)=1/2(x-1)$

Explanation:

$rearrange making x the subject$ $"rearrange making x the subject"$

$2 x + 1 = y$ $2x+1=y$

$\Rightarrow 2 x = y - 1$ $rArr2x=y-1$

$\Rightarrow x = \frac{1}{2} (y - 1)$ $rArrx=1/2(y-1)$

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

$f^{- 1} (x) = \frac{1}{2} (x - 1)$ $f^-1(x)=1/2(x-1)$

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

2 Answers

Explanation:

Explanation:

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

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