Question

if f(x) = x - 7, find f^-1 (3).

Could someone teach me how to solve this? My teacher didn't go over this and I can't find this on my text book.

Answer 1

inverse functions, in general, swap xs and ys

Answer 2

y = x-7

the inverse is found by swapping xs and ys

x = y-7

then "resolve" the equation for y again

Answer 3

or you can just go ahead with the inverse setup and place in the 3 for x and solve

3 = y-7

Answer 4

3 = y - 7?

aren't you supposed to substitute y for 3?

Answer 5

no; the inverse function is still a function of x, so the proper thing to do would be to solve for y again by getting it by its little lonesome

Answer 6

at any rate, all xs are 3s in this case

Answer 7

wait, lemme show you mine lol

Answer 8

AMG i forgot how i did this.

Answer 9

jsut start at the beginning :)

Answer 10

f(x) = x - 7
f(3) = 3 - 7
f(3) = -4
f^-1 (x) = 4

so uhh.. lol

Answer 11

an inverse is not looking for the value of the original "x"; its looking for the value that creates a 3 in the original.

f(x) = y = x-7 ; when x=10, y=3

swap out variables: x = y - 7

resolve: f^-1(x) = y = x + 7

when x=3, y=10

Answer 12

an inverse undoes the original to get you back to x again

Answer 13

when x = 10, y = 3

Swap out the variables:
f(x) = x - 7
y = x - 7
3 = 10 - 7
3 = 3

Resolve:
f^-1(x) = x + 7
y = x + 7

I'm sorry I still can't understand. I'll try to do some research.

Answer 14

alot of the confusion might be in using "x" in both instances.

Answer 15

\[y = f(x)\to\ f^{-1}(y)=x\]a function gets us from x to y; the inverse gets us from y back to x again

Answer 16

the issue is, that by convention we use x as an independant variable. By defining an inverse as a function of x, we create a more confusing learning environment

Answer 17

a my god i can't find anything over the internet, what the heck did this teacher give us >.<

Answer 18

@amistre64 hey! i think i figured it out, how about this?

f(x) = x - 7
f(10) = 10 - 7
f(10) = 3
f^-1(3) = 10

Answer 19

that is actually a good read.