Question

f(x) = 1/2 x+4 then find the value of f -1^(4)

Answer 1

Inverse the function, then apply 4 for x

Answer 2

You can just plug in f(x)=4.

Answer 3

if f(x) =y then switch x and y and solve for y set = 4

Answer 4

it is shorter to just plug in f(x)=4 (then your x is f^(-1)(4).)

Answer 5

so fx = 4 then find the value f -1^(4)

Answer 6

f -1^(x) blank x blank it has that in the first row

Answer 7

f -1^(4)

Answer 8

Example:

\(\color{blue}{\displaystyle f(x)=4x+8}\), find \(\color{blue}{\displaystyle f^{-1}(8)}\).
--------------------------------------
Official approach.
\(\color{blue}{\displaystyle y=4x+8}\)
\(\color{blue}{\displaystyle x=4y+8}\)
\(\color{blue}{\displaystyle x-8=4y}\) \(\\[0.5em]\)
\(\color{blue}{\displaystyle \frac{x-8}{4}=y}\) \(\\[1.1em]\)
\(\color{blue}{\displaystyle f^{-1}(x)=\frac{x-8}{4}}\) (solved for \(f^{-1}(x)\)) \(\\[1.1em]\)
then, plug in x=4. \(\\[1.1em]\)
\(\color{blue}{\displaystyle f^{-1}(8)=\frac{8-8}{4}=0}\)
--------------------------------------
Shortcut.
\(\color{blue}{\displaystyle f(x)=4x+8}\)
\(\color{blue}{\displaystyle 8=4x+8}\)
\(\color{blue}{\displaystyle 0=4x}\)
\(\color{blue}{\displaystyle 0=x}\)
So, \(\color{blue}{\displaystyle f^{-1}(8)=0}\).

Answer 9

so basically do that same thing but, plug in the different equation?

Answer 10

Yes, when you plug in f(x)=4, the solution for x is f^(-1)(4).

Answer 11

http://prntscr.com/d351fp it looks like that not just an equation to fill out

Answer 12

yes, then do what I called the official approach.

Answer 13

ok

Answer 14

First solve for \(f^{-1}(x)\) to find the inverse function.
Swipe x and y, and solve for y. (Your y is now f^(-1)(x).)

The, plug in x=4, to find \(f^{-1}(4)\).

Answer 15

ok

Answer 16

What do the last two blanks on the first line correspond to?

Answer 17

ok

Answer 18

Also, I want to add a brief note about the
difference in methods for finding f^(-1)(4).

In the "official approach" you are swiping f(x) and x,
solve for x (which used to be f(x)), and your f(x) (which used to be x)
is (now) an inverse function. Then, to find f^(-1)(4) you plug in x=4.

So, (if you just needed to find f^(-1)(4)) you can observe that plugging in f(x)=4
(without finding the inverse function), is precisely the same thing (but faster).

Answer 19

but since you do need \(f^{-1}(x)\), we will find the inverse function first.

Answer 20

Do you know how to find the inverse function in general?

Answer 21

yes

Answer 22

Ok,

we will start to apply the same steps to \(f(x)=\frac{1}{2}x+4\).

Answer 23

so basically i multiply 2 x 1/2 to get rid of the fraction?

Answer 24

f(x) + 4?

Answer 25

Well, first (just as matter of convenience, and thus it is typically taught), you write y instead of f(x). So,
\(y=\frac{1}{2}x+4\).

Then, you swipe \(x\) and \(y\). (Like this) \(x=\frac{1}{2}y+4\).

Can you solve for \(y\) now?

Answer 26

so then I would use the inverse function?

Answer 27

yes, but first you got to find this inverse function.

Answer 28

Can you solve this for \(y\) ? \(x=\frac{1}{2}y+4\).

Answer 29

So x = 1/2y + 4. 2x = y + 2 then subtract - from 2x and 2 -2 and then multiply by 1

Answer 30

can you say that again (rephrase) ?

Answer 31

2x=y+2 is correct, I just don't get what exactly you suggest afterwords.

Answer 32

x = 1/2y + 4
2x = y + 2
-2 -2
—————-
2x - 2 = y

2x + 2 = y

y = 2x + 2

Answer 33

why does y=2x-2 turn into y=2x+2 ?

Answer 34

is it not supposed to become a positive sign?

Answer 35

It is not supposed to.

You have y=2x-2 after you subtract (which is correct).
The sign doesn't just all of the sudden, for no reason turn positive if it is negative.

Answer 36

okk

Answer 37

Ok, so this is the inverse function!

Answer 38

\(f^{-1}(x)=2x-2\)

Answer 39

Alrighty so far?

Answer 40

yes

Answer 41

Ok, now you are asked to find \(f^{-1}(4)\).

Answer 42

So, plug in \(x=4\) into \(f^{-1}(x)=2x-2\) ....

Answer 43

\(\large f^{-1}(4)=2\color{red}{\cdot 4}-2={\tiny~}?\)

Answer 44

f -1^(4) = 8 -2 = f-1^(4) = 6

Answer 45

Yes, \(f^{-1}(4)=6\).

Answer 46

I think we are good to go now:)

Answer 47

http://prntscr.com/d35f3o so like this @SolomonZelman

Answer 48

you gave me the same picture ... (?)

Answer 49

that is my final answer

Answer 50

are the answers in the correct boxes

Answer 51

what you posted shows only empty boxes (same as before)

Answer 52

(well, maybe just for me, but I see nothing on there)

Answer 53

@SolomonZelman 1. box i put 2 after x i put - and at the last box it put 2. in the fourth box i put 6