1. Nov 9, 2012

christian0710

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?

2. Nov 9, 2012

lep11

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

3. Nov 9, 2012

christian0710

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

4. Nov 9, 2012

christian0710

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

5. Nov 9, 2012

SammyS

Staff Emeritus

According to the rules for order of operations,

y = 1/2x+½

is equivalent to

y = (1/2)x + ½ .

6. Nov 9, 2012

christian0710

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

7. Nov 9, 2012

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.

8. Nov 9, 2012