Question

If f(x)=2x-1/3 and f^-1 is the inverse of F, what is the value of f^-1(3)

Answer 1

about 1.67

Answer 2

because f^-1(x)=(1/2)x+1/6

Answer 3

well, what's the \(f^{-1}(x) \ of \ 2x-\frac{1}{3} ? \)

Answer 4

How do you get 1/3?

Answer 5

2^-2(3)-1/3
2^-6-1/3
do you want it as a fraction if so this is it unless you want a decimal

Answer 6

1/3?

do you know how to find the \(f^{-1}?\)

Answer 7

@jdoe0001 , I need refreshing on the whole thing.

Answer 8

and I need it in whole number form. I have the answer, I just need to know how to get it. The answer is 5.

Answer 9

if the function is

f(x) = y

y = ax+b

then the inverse is obtained by doing a switcharoo on the variables position, so it becomes

x = ay+b

then you solve for "y"
and is
x = ay+b => x-b = ay => (x-b)/a = y

so the inverse for y= ax+b would be \(\large {y = \frac{x-b}{a}}\)

Answer 10

\[\frac{ 1 }{2 }x+\frac{ 1 }{ 6 } = f ^{-1}(x)\]

Answer 11

\[which is = \frac{ x + \frac{ 1 }{ 3 } }{ 2 }\]

Answer 12

I'm at this point. x=2y-1/3

Answer 13

ok good, simply add the 1/3, than divide the 2

Answer 14

so you will have (x+1/3)/2=f^-1(x)

Answer 15

\[x=\frac{ 2y-1 }{ 3 }\]
Where do you get subtract 1/3?

Answer 16

I see the neg1, but you dont put the 2y over the 3 also?

Answer 17

wait ooooo, thats different

Answer 18

$$
\color{blue}{y} = 2\color{red}{x}-\frac{1}{3}\\
\text{doing a switcharoo}\\
\color{red}{x} = 2\color{blue}{y}-\frac{1}{3}\\
\text{solving for "y"}\\
\cfrac{\color{red}{x}-\frac{1}{3}}{2}=\color{blue}{y} = f^{-1}(x)
$$

Answer 19

no jdoe look, he put it differntly now

Answer 20

wait... a sec

Answer 21

$$
\color{blue}{y} = 2\color{red}{x}-\frac{1}{3}\\
\text{doing a switcharoo}\\
\color{red}{x} = 2\color{blue}{y}-\frac{1}{3}\\
\text{solving for "y"}\\
\cfrac{\color{red}{x}+\frac{1}{3}}{2}=\color{blue}{y} = f^{-1}(x)
$$

Answer 22

Here is the ORIGINAL problem:
\[f(x)=\frac{ 2x-1 }{ 3}\]
FInd \[f ^{-1}(3)\]

Answer 23

\[\frac{ 3x+1 }{ 2 } = f^1(x)\]

Answer 24

hmm, that looks different some :/

Answer 25

f^-1(3)=5

Answer 26

no wonder we did it wrong, you gave it to us wrong.

Answer 27

That is real nice. :(

Answer 28

so yes the answer is 5.

Answer 29

Can you work it out step by step? (patience please)

Answer 30

ok

Answer 31

$$
y=\frac{ 2x-1 }{ 3}\\
\text{doing a switcharoo}\\
x=\frac{ 2y-1 }{ 3}\\\\
\text{solving for "y"}\\
$$

Answer 32

whatever "y" gives you, is your \(f^{-1}(x)\)

Answer 33

Thanks, got it!