## abbie1 Group Title Help!! Let f(x)=7x-13. Find f^-1(x). Let f(x)=x^2-16. Find f^-1(x). one year ago one year ago

1. saifoo.khan Group Title

Do you know how to find an inverse?

2. saifoo.khan Group Title
3. abbie1 Group Title

Okay thanks..

4. hartnn Group Title

ask if you still need help.

5. abbie1 Group Title

I'm still confused..what am I finding the inverse to in my problem?? @hartnn

6. hartnn Group Title

ok, let y=7x-13 now to find the inverse, isolate x =... ? then just replace 'x' and 'y' (you can replace before isolating also.)

7. abbie1 Group Title

-7x=-13-y?? why would there be a y in there??

8. abbie1 Group Title

and then divide the whole thing by -7, but they're going to be fractions.

9. hartnn Group Title

y= 7x-13 add 13 to both sides, then divide by 7 [Let there be fractions, its ok]

10. abbie1 Group Title

So basically you set the problem equal to 7x-13, and either make it equal to y or x?? There is no y in the problem? that's why i am confused

11. abbie1 Group Title

x=-13-y/-7, and then do you want me to solve for x on y=7x-13 or that's what y equals?? So you use x to solve for y and y to solve for x??

12. ohimai Group Title

y = f(x).. They are the same thing

13. abbie1 Group Title

x and y are the same thing??????

14. hartnn Group Title

i considered f(x) = y for simplicity. i'll write out steps so that you can understand. y= 7x-13 y+13 = 7x x = (y+13)/7 now to find inverse function just replace x and y y= (x+13)/7 so your inverse function is $f^{-1}(x)=\dfrac{x+13}{7}$ got this ?

15. ohimai Group Title

f(x) and y are the same thing, so you re-write it as y = 7x-13

16. ohimai Group Title

got that part?

17. abbie1 Group Title

Yes THANK YOU!!!!

18. ohimai Group Title

swop d x for d y.... it becomes x = 7y-13

19. hartnn Group Title

can you do same thing for f(x)=x^2-16. ?

20. ohimai Group Title

yep

21. ohimai Group Title

after swopping, solve for y

22. ohimai Group Title

7y= x+13 y = (x+13)/7

23. abbie1 Group Title

Yes x=4 + sqrt y

24. ohimai Group Title

yes, but u have to swop d x and d y back... final answer would be y = 4 + sqrt(x)

25. hartnn Group Title

did u simplify like this ? $\sqrt{16+y}=4+\sqrt y$ no, thats incorrect.

26. abbie1 Group Title

by d do you mean the?

27. ohimai Group Title

yep

28. abbie1 Group Title

sqrt. y+16=x^2 (Root over y+16)

29. hartnn Group Title

yeah, the inverse function will be $f^{-1}(x)=\sqrt{x+16}$ no further simplification possible.

30. hartnn Group Title

ok ? got it ?

31. abbie1 Group Title

Oh got it!!!