Question

PLEASE HELP!!!!!

If f(x) = (1/3)x - 4, find (f^(-1))(-3).

Answer 1

You'd multiply (-1) by 1/3 and then multiply the result with -3.

Answer 2

You'd multiply 1/3 then subtract 4 *

Answer 3

Yes, I'm a bit confused.

Answer 4

oh lol yeah

Answer 5

thats much easier

Answer 6

Oh wait, yes, didn't see that.

Answer 7

That's okay, don't worry about it! @Australopithecus

Answer 8

f(x) = (1/3)x - 4
in this case

set y to x and x to y and solve for y

x = (1/3)y - 4
=
0 = (1/3)y - 4 - x
=
-(1/3)y = - 4 - x
=
y = -3(- 4 - x)

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

Answer 9

there that is the answer

Answer 10

i switch the variables just to make it easier to follow

Answer 11

Wow! Thank you SO much! I really do appreciate it! Thank you, as well, to everyone else who helped!

Answer 12

now i need to pass out I cant believe i didnt notice it was an inverse function

Answer 13

Sorry - what do you mean? Are you saying that you did the steps incorrectly?

Answer 14

no I did it correctly the negative exponent on the function means it is an inverse function

Answer 15

OH, okay. That's good :)

Answer 16

which means that it is a graph were the y becomes the x and the x becomes the y

Answer 17

you can only do this on functions that are 1 to 1, that is pass the horizontal line test

Answer 18

since what you are graphing in linear and passes the test thus you can determine its inverse, some functions such as trigonometric functions we need to restrict the domain to determine the inverse.

Answer 19

Okay.

Answer 20

for example

sin(x)
the graph is



If we were to flip this graph sin(x) we would get something like this



which doesn't pass the vertical line test, which means that if you draw a line vertically through a graph and it passes the line of the graph more than once then you do not have a function

thus we restrict its domain from [-pi/2,pi/2] so that it is a function



now it passes the vertical line test and the thus the horizontal line test