Question

PLEASE HELP!!
If f^-1(x)=4/3x+8, what is f(x)??

Answer 1

so the inverse of a function sends the x to y and y to x, so the inverse of the inverse, does what?

Answer 2

Replace f^-1 by \(x\)
Replace x by \(f(x)\)
then, solve for \(f(x)\)

Answer 3

@FibonacciChick666 switch the variables

Answer 4

yep, so f^-1(x) let's call that y', we can call the x for the inverse function x'. Now since we swap the x and the y just to get the inverse function, can you tell me what y'= in terms of the original function?

Answer 5

If that doesn't make sense tell me, I'll try to explain better.

Answer 6

y is = 4/3x+8

Answer 7

ok, so y'=4/3x'+8

Answer 8

so that we can use x and y for f(x)

Answer 9

is the answer is f(x)=3/4x-8

Answer 10

That's possible, but I have not done it yet

Answer 11

oh okay

Answer 12

so for me personally, to avoid annoying variable confusion. I name the inverse g(x). So g(x)=x for f(x) and the x in g(x)=f(x) or y in the original f(x)

Answer 13

so rewriting in terms of f(x)
\[g(x):=~~~x=\frac{4}{3}y+8\]

Answer 14

so now I solve for y. Then I will be done

Answer 15

so can you see if using that you get the same answer? I think it may be different

Answer 16

ok, I know I'm being confusing so, to get the inverse you swap x and y right? well to get the inverse of the inverse, ie the original functions, you swap the variables again.

Answer 17

yea i know

Answer 18

ok so solve: \[ x=\frac{4}{3}y+8\] for y and see if you get the same answer

Answer 19

( you shouldn't)

Answer 20

show your steps, I think I know where you are going wrong

Answer 21

\[x=\frac{ 4 }{ 3 }y+8\]

Answer 22

\[-3x=4y+8\]

Answer 23

why do you have a minus 3x?

Answer 24

\[f(x)=\frac{ 3 }{ 4}x-8\]

Answer 25

that is an incorrect step

Answer 26

because i put 3 outside the = and change to -3

Answer 27

help me

Answer 28

yea... that's not how it works

Answer 29

ok so \[x=\frac{4}{3}y+8\] You have to reverse the order of operations to solve for y. So if you use PEMDAS, the reverse is SADMEP. So we start by undoing any addition or subtraction. Do we have any?

Answer 30

can you show mw the 2nd step?? maybe i might figure it out

Answer 31

well, first answer, is there any addition going on?

Answer 32

yes

Answer 33

so how do we undo addition?

Answer 34

what is the opposite of addition?