Question

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

Answer 1

Do you know how to find an inverse?

Answer 2

https://www.khanacademy.org/math/trigonometry/functions_and_graphs/fucntion_inverses/v/function-inverse-example-1

Answer 3

Okay thanks..

Answer 4

ask if you still need help.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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??

Answer 12

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

Answer 13

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

Answer 14

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 ?

Answer 15

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

Answer 16

got that part?

Answer 17

Yes THANK YOU!!!!

Answer 18

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

Answer 19

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

Answer 20

yep

Answer 21

after swopping, solve for y

Answer 22

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

Answer 23

Yes x=4 + sqrt y

Answer 24

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

Answer 25

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

Answer 26

by d do you mean the?

Answer 27

yep

Answer 28

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

Answer 29

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

Answer 30

ok ? got it ?

Answer 31

Oh got it!!!