Question

For the function \(\normalsize{f(x) = (8-2x)^2}\) ,find \(\normalsize{f-1}\) . Determine whether \(\normalsize{f-1}\) is a function.

Answer 1

Well to find the inverse, here are some steps:

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 2

Ok. Let me see what I can get. If not, I'll need serious help. Cuz this is what one of my answer choice looks like:
\[f ^{-1}(x) = \frac{ 8\pm \sqrt{x} }{ 2 }\]

Answer 3

I seem not to understand this problem.

Answer 4

This page helps you determine if a function has an inverse

http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/vertandhorizlinetests.html

I've highlighted the portion in question (see attached)

Answer 5

Yes, that seems to be correct, to find out if it's a function you can do the horizontal line test.

Answer 6

So, pretty much all I have to do is like find out if it intersects or not?

Answer 7

What about solving though?

Answer 8

you dont need to do that.

Answer 9

if its a function then no one x can point to more than one y

Answer 10

how many answers are there for f(2)?

Answer 11

hint: the \(\pm\) gives it away.

Answer 12

you mean \(f^{-1}(2)\)

Answer 13

yes \(\uparrow\)

Answer 14

I thought that would make it easier, maybe not.:(

Answer 15

that's how I would do it. you have the inverse...use it

Answer 16

@YanaSidlinskiy do you understand? Also, I think you are making it hard on yourself with the normal size stuff

`\(\normalsize{f}\)` -> \(\normalsize{f}\)
`\(f\)` -> \(f\)

Answer 17

unless you change to something different, and need to go back, there is no point.

Answer 18

Sorry..I was afk. Wow! It's crazy let me think.

Answer 19

Ok. I have 4 multiple choice answers. It's half and half. There's 2 that "is a function" and "is not a function"

Answer 20

so if f^-1 is a function, then you are not allowed to get two answers to f^-1(x) for any x.


what is f^-1(2)?

Answer 21

The other one is:
\[\pm \sqrt{\frac{ 8+x }{ 2 }}\]

Answer 22

we dont need the options, we know the answer.

Answer 23

better yet, how many answers does f^-1(2) give?

Answer 24

Umm..Like 1 or 2. Right?

Answer 25

\[f ^{-1}(x) = 4 \pm \frac{ \sqrt{x} }{ 2 }~~~ f ^{-1}(2) =?\]

Answer 26

Ok, I was being stupid on this question. Anyways I got the answer:D Thanx for all your help!!!:D Everyone!!!!!!!!!!!! I seriously do appreciate it!

Answer 27

\(\huge\cal\color{Lime}{Thank~you!!!!!!!!}\)

Answer 28

is it a function?