## Barrelracing one year ago Which of the following expressions is the inverse of the function y= x+5/7 a) y= x+7/5 b) y= x-5/7 c) y=5x-7 d) y=7x-5

1. freckles

solve for x

2. freckles

if the equation is y=x+5/7 to do that you just need to subtract 5/7 on both sides if the equation is y=(x+5)/7 I would first multiply 7 on both sides and if is this equation you have one more step remaining after that

3. Barrelracing

its the first one but im not sure how to divide the 5/7 to both sides..sorry can u help?

4. freckles

no subtraction is not division

5. freckles

Here is an example: $y=x+a \\ \text{ Subtract } a \text{ on both sides } \\ y-a=x \\ \text{ or other way around } x=y-a \\ \text{ then you can interchange } x \text{ and } y \\ y=x-a \text{ this is the inverse of } y=x+a$

6. Barrelracing

sorry read it wrong so it would be 5/7y = x?

7. freckles

well you didn't exactly subtract 5/7 on the left hand side it appears you multiply 5/7 on left hand side

8. Barrelracing

im so confused can u just do this one for me so I can use it as an example for my other problems? im not cheating it would be easier for me to understand. im sorry.

9. freckles

oh so you didn't understand the example above either?

10. Barrelracing

oh wait got it hold on

11. Barrelracing

y-5/7=x?

12. freckles

$\text{ pretend } a=\frac{2}{3} \\ y=x-\frac{2}{3} \text{ is the inverse of } y=x+\frac{2}{3} \\ \text{ if work needs \to be shown we can go through the process again } \\ \text{ pretend we have } \\ y=x+\frac{2}{3} \\ \text{ subtract } \frac{2}{3} \text{ on both sides } \\ y-\frac{2}{3}=x \\ x=y-\frac{2}{3} \\ \text{ interchange } x \text{ and } y \\ y=x-\frac{2}{3} \\ \text{ So we know } y=x-\frac{2}{3} \text{ is the inverse of } y=x+\frac{2}{3}$

13. freckles

14. freckles

$y=x+\frac{5}{7} \\ \text{ subtract} \frac{5}{7} \text{ on both sides } \\ y-\frac{5}{7}=x \\ x=y-\frac{5}{7}$ yep now just interchange x and y

15. Barrelracing

interchange?

16. freckles

replace x with y and y with x

17. freckles

pull the old switch a roo

18. UsukiDoll

y= x+5/7 switch the x and the y and then solve for y

19. freckles

$y=x-\frac{5}{7}$

20. freckles

you can solve for x then switch but either way

21. UsukiDoll

I was taught to switch first then solve for y :)

22. Barrelracing

y = x-5/7

23. UsukiDoll

but that works too... even though I got used to one technique @freckles

24. freckles

here is another example @Barrelracing of finding inverse of a linear function $y=\frac{x+5}{7} \\ \text{ multiply both sides by } 7 \\ 7y=x+5 \\ \text{ then subtract} 5 \text{ on both sides } 7y-5=x \\ \text{ now interchange } x\text{ and } y \\ 7x-5=y \\ y=7x-5 \text{ is the inverse of } y=\frac{x+5}{7}$

25. freckles

there is a reason I like to do the switch step last @UsukiDoll

26. freckles

but a linear example is not the best example to show why

27. anonymous

By the way @Barrelracing you look wonderful.