Question

Let f(x) = x2(squared) − 81. Find f−1(f to the power of -1)(x)

Answer 1

@Plasmataco

Answer 2

A)-6
B)-3
C)3
D)6

Answer 3

Like my picture :]

Answer 4

I like it, been to busy trying to get work done to check chat sorry

Answer 5

Ayyy lmao Tysm :3

Answer 6

Also I'm not sure i'll tag a friend :0

Answer 7

@KamiBug

Answer 8

@Preetha

Answer 9

Sorry for tagging you guys I just felt like I needed to try and help in some way :D

Answer 10

\(\color{#000000}{ \displaystyle f(x)=x^2 -81 }\)
and you want the inverse function \(\color{#000000}{ \displaystyle f^{-1}(x) }\) correct?

Answer 11

I will have to dissapoint you as a mathematician, and to tell you something nice as a student doing homework. There won't be an inverse.

Answer 12

Ok, as you probably know, the inverse of the function
\(f(x)={\{\rm some~expression~with~x\}}\), is generally found
by the following steps:

1) Replace f(x) with y.
2) Swipe your x and y.
3) Solve your (new) expression for y.
4) Having solved for y, write this y as \(f^{-1}(x)\)
(Because this y is the inverse function).

Answer 13

You're really smart xD

Answer 14

i'm super confused

Answer 15

Now, if you were to try this on a function of a form:
\(\color{#000000}{ \displaystyle f(x)=x^2 -a^2 }\)

Then, you would start this way:
\(\color{#000000}{ \displaystyle y=x^2 -a^2 }\) (step 1)
\(\color{#000000}{ \displaystyle x=y^2-a^2 }\) (step 2)
\(\color{#000000}{ \displaystyle x+a^2=y^2 }\) (step 3)

you can take the square root of both sides, but still don't achieve the desired result
\(\color{#000000}{ \displaystyle \sqrt{x+a^2}=\sqrt{y^2} }\)

and the left side is NOT just y, rather absolute value of y (via the definition of the absolute value).
\(\color{#000000}{ \displaystyle \sqrt{x+a^2}=|y| }\)

Answer 16

The most you can say is:
\(\color{#000000}{ \displaystyle \left|f^{-1}(x)\right|=\sqrt{x+a^2} }\)

but you can't solve for the inverse as a single function.

Answer 17

I think i made this so confusing because i put the answer choices from the wrong question ':D

Answer 18

hehe

Answer 19

Ok, I will add the last note, to test a function for whether or not it's inverse exists. But I will add it only on a condition that you know what a one-to-one function is. Do you know?

Answer 20

\[\pm \sqrt{x+81}\]
\[9^{\sqrt{x}}\]
\[\frac{ 1 }{ x ^{2}-81 }\]
\[\frac{ x _{2} }{ 81 }\]

Answer 21

no clue, it's my first week in Algebra 2

Answer 22

Have you ever done problems finding inverse functions?

Answer 23

Or is this the first time?

Answer 24

It's my first time and i need to have it done by tonight and work in three other classes

Answer 25

We are all busy people here.
Ok, previously, I wrote the general steps of finding the iverse function. Can you please attempt an example problem: \(f(x)=x+4\)?

Answer 26

The inverse of the function \(f(x)=\rm \{some~expression~with~x\}\),
is generally found by the following steps:

1) Replace f(x) with y.
2) Swipe your x and y.
3) Solve your (new) expression for y.
4) Having solved for y, write this y as f\(^{-1}\)(x). (since this y is inverse function).

Answer 27

But don't i have to know what X is ?

Answer 28

Please try to preform these steps on f(x)=x+4.
No, you don't have to know what x is. It could be anything, since it is the independent variable.

Answer 29

So, is sit y=x-4 ?

Answer 30

is it*

Answer 31

that would be it. and then re-write this as \(f^{-1}(x)=x-4\).
So, \(f^{-1}(x)\) instead of the y, since it is the inverse function.

Answer 32

Ok, can you do one more for me please?
f(x)=5x-2

Answer 33

Would you change that to y=5x-2 and then do 5x=y-2 or x=5y-2 ??

Answer 34

????

Answer 35

f(x)=5x-2
y=5x-2
x=5y-2
x+2=5y
(x+2)/5=y

So, \(f^{-1}(x)=(x+2)/5\)

Answer 36

Ok ?

Answer 37

uh, ohkai

Answer 38

Ok, now let's try
f(x)=x^2-81

Answer 39

Can you do the first 2 steps for me please?

Answer 40

I think i got the answer, but i don't understand the \[\pm\] symbol

Answer 41

Ok, can you show your work?

Answer 42

I will tell you where you are having a problem

Answer 43

\[y=\sqrt{81+x}\] is what i got

Answer 44

That is not correct.

Answer 45

oh, sorry yeah gimme one second to get it all in

Answer 46

why not ?

Answer 47

sure, take your time.

Answer 48

Can you type your work. All of it, please.

Answer 49

I want to see all steps

Answer 50

\[y=x ^{2}-81\]
\[x=y ^{2}-81\]
+81 +81
\[x+81=y ^{2}\]
\[\sqrt{x+81}=\sqrt{y ^{2}}\]
\[y=\sqrt{x+81}\]

Answer 51

I am sure you are familiar with the absolute value function, (right?)
So, there is a defintion for the absolute value:
\(\color{#000000}{ \displaystyle \sqrt{z^2}=\left|z\right| }\)

Answer 52

So, actually, after you take the
square root of both sides to get:

\(\color{#000000}{ \displaystyle \sqrt{x+81}=\sqrt{y^2} }\)

And by the definition of the absolute
value you are going to get:
\(\color{#000000}{ \displaystyle \sqrt{x+81}=|y| }\)

You know that in general, if \(\color{#000000}{ \displaystyle |z|=5 }\),
then \(z=\pm 5\). By this convention, you have,

\(\color{#000000}{ \displaystyle \pm \sqrt{x+81}=y }\)

And since y is the inverse function you write,
\(\color{#000000}{ \displaystyle f^{-1}(x)= \pm \sqrt{x+81} }\)

Answer 53

There is a technical error with saying that this is a valid inverse and with saying that the inverse of x^2-81 exists, because both of these statements are wrong!

Answer 54

well, i'm gonna go with that one because none of the above isn't an option and i still have too much other work to do. But i understand a lot better, thank you (:

Answer 55

Yes, go with that one. I was just going to say that don't worry about this technicality now, except for that I didn't have time because I lagged the 51st time.

Answer 56

Enjoy, and, best of luck to your mathematics!

Answer 57

thank you (:

Answer 58

It's true that the given function doesn't have an inverse (if you were to graph y=x^2 - 81, you 'd see a parabola that opens upward. Drawing a horiz. line thru this graph would intersect the graph in 2 places, which means that y = x^2 - 81 has no inverse. However, you could restrict the domain of y = x^2 - 81 to [0, infinity), in which case
this derived function WOULD have an inverse.

Answer 59

0.o my brain hurts. I'm gonna post another question because i'm stupid xD

Answer 60

Sorry about your brain hurting. But kindly stop using "I'm stupid" as a reason or an excuse for anything. Why shoot yourself in the foot if you don't need or want to ? Ouch.

Answer 61

..

Answer 62

Please repost your latest question, but separately from this post. Thx.