## anonymous one year ago 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

1. anonymous

@jim_thompson5910

2. jim_thompson5910

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

3. anonymous

The second one

4. UsukiDoll

lack of sleep .. T_T

5. jim_thompson5910

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

6. UsukiDoll

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

7. jim_thompson5910

either way works

8. anonymous

9. UsukiDoll

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

10. UsukiDoll

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

11. UsukiDoll

$\large 3x=y-2$

12. UsukiDoll

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

13. UsukiDoll

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

14. anonymous

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

15. jim_thompson5910

3x and 2 are NOT like terms

16. UsukiDoll

ummmm 3x+2 is not combinable

17. jim_thompson5910

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

18. anonymous

Oh. Sorry.

19. UsukiDoll

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

20. anonymous

Ok... how do I isolate y.

21. UsukiDoll

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

22. jim_thompson5910

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

23. jim_thompson5910

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

24. UsukiDoll

:( ! why jim why

25. jim_thompson5910

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

26. anonymous

Oh, thank you Jim.

27. jim_thompson5910

28. anonymous

Thank you both.

29. UsukiDoll

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 $\Large 3x+2=y$

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