## anonymous one year ago if f(x)=-6x+6, then f^-1(x)

1. UsukiDoll

any attempts?

2. anonymous

solve $x=-6y+6$ for $$y$$ in two steps

3. UsukiDoll

that's what I was thinking.. swap the variables.. solve for y and then replace y with the f inverse notation .

4. anonymous

at least that is the math teacher way the thinking way is to recognize that$f(x)=-6x+6$ means a) multiply by $$-6$$ then b) add $$6$$ inverse will do the opposite operations in reverse order

5. anonymous

but solving $x=-6y+6$ for $$y$$ takes two steps, so it is just as quick as thinking

6. anonymous

I'm confused

7. anonymous

can you work through it with me?

8. anonymous

please? all my attempts arent working out

9. anonymous

@UsukiDoll

10. anonymous

Just follow these easy steps: To find the inverse: Replace f(x) with y Switch x's and y's, so put x where y is and x where y is. Solve for y Replace y with f^-1(x)

11. anonymous

I know the steps but I usually get stuck when solving for y

12. anonymous

$y=-6x+6$ $x=-6y+6$ what would your first step be to solving for y?

13. anonymous

Try your best, don't be afraid to make mistakes

14. anonymous

get rid of + 6 by subtracting six from both sides

15. anonymous

There you go, good job, so we have $x-6 = -6y$ now what?

16. anonymous

divide by negative 6

17. anonymous

Good! $y = \frac{ -(x-6) }{ 6 }$ you may simplify that now

18. anonymous

how?

19. anonymous

As in you can distribute the negative sign, and get $y = \frac{ -x+6 }{ 6 } \implies \frac{ 6-x }{ 6 }$ so what's our final step?

20. anonymous

What should we replace y with :)

21. anonymous

the rule for negative functions

22. anonymous

|dw:1436932582839:dw|

23. anonymous

$f^{-1}(x) = \frac{ 6-x }{ 6 }$ yup :)

24. anonymous

Not so bad right? Just have to try it and you'll start getting it!

25. anonymous

it helps to talk it out, I probably would've taken a lot longer to get that on my own

26. anonymous

I think that is the best way of learning to :)

27. anonymous

thanks for your help, i understand it better, not completely yet but making progress

28. anonymous

No problem, take care!