abbie1 2 years ago Help!! Let f(x)=7x-13. Find f^-1(x). Let f(x)=x^2-16. Find f^-1(x).

1. saifoo.khan

Do you know how to find an inverse?

2. saifoo.khan
3. abbie1

Okay thanks..

4. hartnn

ask if you still need help.

5. abbie1

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

6. hartnn

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

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

8. abbie1

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

9. hartnn

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

10. abbie1

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

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

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

13. abbie1

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

14. hartnn

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

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

16. ohimai

got that part?

17. abbie1

Yes THANK YOU!!!!

18. ohimai

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

19. hartnn

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

20. ohimai

yep

21. ohimai

after swopping, solve for y

22. ohimai

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

23. abbie1

Yes x=4 + sqrt y

24. ohimai

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

25. hartnn

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

26. abbie1

by d do you mean the?

27. ohimai

yep

28. abbie1

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

29. hartnn

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

30. hartnn

ok ? got it ?

31. abbie1

Oh got it!!!