Which of the following expressions is the inverse of the function y = x - 2 / 3?
y = 3x + 2
y = 2x + 3
y = x - 3 / by 2
y = x + 2 / by 3

Question

Which of the following expressions is the inverse of the function y = x - 2 / 3?
y = 3x + 2
y = 2x + 3
y = x - 3 / by 2
y = x + 2 / by 3

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

Is the original
$$\Large y = x - \frac{2}{3}$$
or is the original
$$\Large y = \frac{x-2}{3}$$

anonymous · Answer

The second one

usukidoll · Answer

lack of sleep .. T_T

jim_thompson5910 · Answer

$$\Large y = \frac{x-2}{3}$$

swap x and y

$$\Large x = \frac{y-2}{3}$$

now solve for y

usukidoll · Answer

hmmm I would get rid of the denominator by multiplying 3 all the way first and then swap x and y.

jim_thompson5910 · Answer

either way works

anonymous · Answer

I'm not sure what to start with when solving for y.

usukidoll · Answer

$$\Large 3y = (3)\frac{x-2}{3} \rightarrow 3y=x-2$$

usukidoll · Answer

then swap x and y . In other words switch places ...

usukidoll · Answer

$$\large 3x=y-2$$

usukidoll · Answer

and then solve for y...this would be much easier because I got rid of the fraction first by multiplying the entire equation by 3

usukidoll · Answer

so what do we need to do to have y by itself

anonymous · Answer

3x=y-2
+2      +2

5x=y

jim_thompson5910 · Answer

3x and 2 are NOT like terms

usukidoll · Answer

ummmm 3x+2 is not combinable

jim_thompson5910 · Answer

you cannot say 3x+2 turns into 5x or 5

anonymous · Answer

Oh. Sorry.

usukidoll · Answer

because 3x has a number and variable   2 is just a number... it can't be combined

anonymous · Answer

Ok... how do I isolate y.

usukidoll · Answer

y has to be by itself... 
$$\large 3x=y-2 $$
so what do we need to do to have y by itself... y is destined to be alone xD

jim_thompson5910 · Answer

unheard, when you added 2 to both sides, you were on the right path

jim_thompson5910 · Answer

3x = y - 2
  +2     +2


3x + 2 = y


y = 3x + 2

usukidoll · Answer

:( ! why jim why

jim_thompson5910 · Answer

you just leave 3x+2 as it is since you cannot combine those terms

anonymous · Answer

Oh, thank you Jim.

jim_thompson5910 · Answer

she already had it usukidoll

anonymous · Answer

Thank you both.

usukidoll · Answer

jim's version would have required fractions to be split up

$$\Large x = \frac{y-2}{3} \rightarrow x = \frac{y}{3}-\frac{2}{3}$$

$$\Large x + \frac{2}{3} = \frac{y}{3}$$
and then multiply 3 throughout the equation... too long...but another way to check
$$ \Large 3x+2=y$$