anonymous
  • anonymous
Help!! Let f(x)=7x-13. Find f^-1(x). Let f(x)=x^2-16. Find f^-1(x).
Mathematics
katieb
  • katieb
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saifoo.khan
  • saifoo.khan
Do you know how to find an inverse?
saifoo.khan
  • saifoo.khan
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/fucntion_inverses/v/function-inverse-example-1
anonymous
  • anonymous
Okay thanks..

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hartnn
  • hartnn
ask if you still need help.
anonymous
  • anonymous
I'm still confused..what am I finding the inverse to in my problem?? @hartnn
hartnn
  • 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.)
anonymous
  • anonymous
-7x=-13-y?? why would there be a y in there??
anonymous
  • anonymous
and then divide the whole thing by -7, but they're going to be fractions.
hartnn
  • hartnn
y= 7x-13 add 13 to both sides, then divide by 7 [Let there be fractions, its ok]
anonymous
  • anonymous
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
anonymous
  • anonymous
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??
anonymous
  • anonymous
y = f(x).. They are the same thing
anonymous
  • anonymous
x and y are the same thing??????
hartnn
  • 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 ?
anonymous
  • anonymous
f(x) and y are the same thing, so you re-write it as y = 7x-13
anonymous
  • anonymous
got that part?
anonymous
  • anonymous
Yes THANK YOU!!!!
anonymous
  • anonymous
swop d x for d y.... it becomes x = 7y-13
hartnn
  • hartnn
can you do same thing for f(x)=x^2-16. ?
anonymous
  • anonymous
yep
anonymous
  • anonymous
after swopping, solve for y
anonymous
  • anonymous
7y= x+13 y = (x+13)/7
anonymous
  • anonymous
Yes x=4 + sqrt y
anonymous
  • anonymous
yes, but u have to swop d x and d y back... final answer would be y = 4 + sqrt(x)
hartnn
  • hartnn
did u simplify like this ? \[\sqrt{16+y}=4+\sqrt y \] no, thats incorrect.
anonymous
  • anonymous
by d do you mean the?
anonymous
  • anonymous
yep
anonymous
  • anonymous
sqrt. y+16=x^2 (Root over y+16)
hartnn
  • hartnn
yeah, the inverse function will be \[f^{-1}(x)=\sqrt{x+16}\] no further simplification possible.
hartnn
  • hartnn
ok ? got it ?
anonymous
  • anonymous
Oh got it!!!

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