INVERSE FUNCTION....MATH QUESTION.....10 POINTS!!! read?

Question

Says:

Determine the inverse functions for the functions below. Begin by switching variables in the original function, then solving for the 'new' y.

state the Invariant.

1. Y = (-1/2)x + 7

10 points!!

Someone answered:

Y = (-1/2)x + 7

X=-1/2y+7

simplify y:

1/2y=-x+7

y=-2x+14 (dont understand how they got this, please explain in detail so i will understand)

10 pts!!

:)

Answer 1

(1/2)y=-x+7

multiply both sides by the reciprocal of 1/2, which is 2

y=2(-x+7)

y=-2x+14,  

Answer 2

Your note:

Someone answered:

Y = (-1/2)x + 7

X=(-1/2y)+7 ..............etc.

add -7 to both sides

x-7=(-1/2y)+7-7=(-1/2)y

multiply each side by -2

-2(x-7)=(-1/2)y*-2=y

or

-2x+14=y

or y=-2x+14

whatever you do to one side of the equation,

do to the other.  To get y (or x) alone.

Hope this helps you.

Answer 3

If you have a function like y = (-1/2)x + 7, an easy way to find its inverse is to interchange the variables (so change the x to a y and the y to an x).  In this case, this gives you x = (-1/2)y + 7.  While this is a valid way to express the inverse function, it would be nice to write it in a more standard form; this is what the person did in their answer:

x = (-1/2)y + 7

Add (1/2)y to both sides:

x + (1/2)y = 7

Subtract x from both sides:

(1/2)y = -x + 7

Multiply through by 2:

(2/2)y = -2x + 14

But (2/2)y is just y, so this becomes:

y = -2x + 14

This is the standard slope-intercept form for the equation of a line, so we can stop here.

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