Converting Functions: From y(x) to x(y) and the Algebra Behind It

[christian0710]

going from x(y) to y(x), please help :)

If we have a function y=1/2x+½ how come if we isolate x as a function of y on a calculator we get x=2y-1??

i get the 2*y but not the -1
What algebra is needed to get from y(x) to x(y) in this case?

 

[lep11]

Multiply the original equation by 2 and then subtract 1 from both sides.
y=½x+½
2y=x+1
x=2y-1

 

[christian0710]

Woaa, i see :D
So normal algebra by isolating x instead of y, does not work when there are two variables?

 

[christian0710]

How come i would get x=y/½ -½ if i use the regular add, subtract, multiply and divide operations?

 

[SammyS]

How come i would get x=y/½ -½ if i use the regular add, subtract, multiply and divide operations?

According to the rules for order of operations,

y = 1/2x+½

is equivalent to

y = (1/2)x + ½ .

 

[christian0710]

Hmm. I don't see the difference between the two steps (except for the brackets?)

 

[bossman27]

What SammyS did is a perfectly normal operation.

You could also do it like this, keeping in mind that you'll get the same thing and that the other way is even easier.

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

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

Now multiply both sides by two (note that this is the exact same thing as "dividing both sides by 1/2")

2y-1 = x

To show why dividing by 1/2 is the same thing:

$\frac{\frac{1}{2}x}{\frac{1}{2}} = \frac{y}{\frac{1}{2}} - \frac{\frac{1}{2}}{\frac{1}{2}}$

Note that 1/2 divided by 1/2 is 1, so y divided by 1/2 is 2. Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction.

 

[christian0710]

Ahh Now i see!
Thank you for the help, now I can continue on my double integral of 3-D shapes (I often forget the simple algebra so I'm trying to strengthen it by doing it all by hand) :)