Question

Find the inverse of the function. f(x)=^2+4/3

Answer 1

I assume it's f(x) = x^2 + 4/3

Answer 2

To the find the inverse, let's rewrite the equation, replacing f(x) with y.
y = x^2 + 4/3

Answer 3

http://media.education2020.com/evresources/1103-02-06-00-00_v2_files/i0030000.jpg

Answer 4

Then, swap the places of x and y. So you'll get x = ...
Then, solve for y again. Finally, replace y with f^(-1)(x), which means inverse of a function.

Answer 5

Oh, ok. f(x) = (x^2 + 4)/3
Same deal, can you follow my steps?

Answer 6

okay let me see

Answer 7

okay so you said swap the places of x and y..so 3/x^2+4?

Answer 8

i mean o x=3/x^2+4

Answer 9

Err, no try again. So we have this:
\[y = \frac{x^2 + 4}{3}\]

Answer 10

This is what I mean by swap places:
\[x = \frac{y^{2} + 4}{3}\]

Answer 11

ohh okay so umm whats next?

Answer 12

Solve for y. We need to get this in the correct form for the inverse notation.

Answer 13

i forgot how to solve.. do i just subtract 3 with 4 and y^2?

Answer 14

No. Let's get rid of the 3 in the denominator first. How can you do that?

Answer 15

i dont know :(

Answer 16

do i switch it again?

Answer 17

No, we're not switching it again. We're just solving for y. How about multiplying both sides by 3?

Answer 18

okay so i multiply 4*3 which is 12 and what about the y^2?

Answer 19

That is incorrect. Do you not know how to simplify fractions?
\[x(3) = (\frac{y^2 + 4}{3})(3)\]
\[3x = y^2 + 4\]

Answer 20

no i dont. i really suck at this. okay so you subtract 3 on each side or no?

Answer 21

i mean for the next step you did

Answer 22

I multiplied both sides by 3. It will cancel on the right side because 3/3 = 1. And x will just turn into 3x.
Now, on the newest equation, how can we get y by itself?

Answer 23

Is there something you can subtract?

Answer 24

is it 4?

Answer 25

Yes, rewrite the equation now.

Answer 26

okay

Answer 27

wait do i subtract 4 on the 3x?

Answer 28

3x=y^2+4
-4 -4

Answer 29

like that?

Answer 30

Yes yes. What do you get now.

Answer 31

-1

Answer 32

i mean 1 lol

Answer 33

1=y^2

Answer 34

No, you can't subtract terms with different variables. 3x can only be added or subtracted by terms with x in them.

Answer 35

\[3x - 4 = y^2\]
Do you know how to get rid of the power on the y now?

Answer 36

no

Answer 37

oh wait hold on

Answer 38

so is y^2 subtracted by 4 then? and 4 and 4 are crossed out

Answer 39

Yeah, on the right side. The 4's got cancelled out because we subtracted 4 from both sides.

Answer 40

Do you know about square roots?

Answer 41

yes

Answer 42

Good. Square root both sides so we can get rid of the squared term on the y.

Answer 43

square y^2? and 3?

Answer 44

im sorry but you could show me how you did it

Answer 45

nvm idk..