Question

Can I please have help? @campbell_st

Answer 1

@amistre64 @e.mccormick

Answer 2

Can we start with question 2

Answer 3

Please help me, I beg

Answer 4

@phi @ganeshie8

Answer 5

any functions of more than 1 operation come to mind?

Answer 6

6x + 1h - 1

Answer 7

thats more of a function of 2 variables, which isnt what i think the question is asking for

Answer 8

How, so should I do it?

Answer 9

lets say f(x) is the name of our function:

we define f(x) by some rule or mathematical sentence: f(x) = (x-1)/4 is some definition for f(x) that provides us with 2 operations (addition and division).

agreed?

Answer 10

ok

Answer 11

if this is truely a function then if f(a)=f(b) only if a=b; let a,b be any real number and set up the situation that f(a) = f(b) and see if we can reduce it to a=b

Answer 12

Ok, I understand

Answer 13

(a-1)/4 = (b-1)/4

a-1 = b-1

a = b

Answer 14

Is (a-1)/4 = (b-1)/4 our function or f(x) = (x-1)/4 is?

Answer 15

our function has a name, and a definition. we use the definition to prove that our function is actually a function

Answer 16

I see...okay!

Answer 17

so our definition proves a = b, correct?

Answer 18

your materials should define how to prove a function is a function; your job is to pretty much repeat it in your explanation.

Answer 19

Whizh question does it answer, 2 or 3 or 4?

Answer 20

the one that says to prove the function is a function of course ....

Answer 21

one question says top define a function with 2 operations

another says to prove its a function

another says to solve for a specific value of x

Answer 22

im having issues with how i defined a function; since its based from memory ... how does your material define the method for proving a function is a function?

Answer 23

example:

f(x) = x^2 since for some x=a: a^2 only has one value associated with it.

Answer 24

but say a = -2, and b=2

a^2 = b^2 does not imply that a=b

Answer 25

Okay it just implies a^2 = b^2 nothing else

Answer 26

right, so its not a good memory recollection on how to prove a function is a valid function :)

Answer 27

Understood

Answer 28

@amistre64 the definition you gave is for one-to-one functions. Still a valid way to show your function is indeed a function, though.

Answer 29

yeah, but its only valid for a 1-1 function .... was trying to recall a more general proof.

Answer 30

spose our function is: x*x + 1 2 operations, it is a function. how to show it?

Answer 31

I am lost, what was our function?

Answer 32

Right. The one-to-one definition is the horizontal line test, whereas any function would be the vertical line test. In terms of math, that would be something like
\[f(x)\text{ is a function if you can map a single output to any one input}\]
if that makes sense...

Answer 33

'our function' is still defined up above

Answer 34

the last question makes me wonder if we are not spose to make an invertible function to start with.

Answer 35

Can we do that

Answer 36

we can, but you really need to consult your material to see how they define a 'true' function.

Answer 37

this assessment is just trying to get you to repeat what the lesson material mentions.

Answer 38

It didn't state a thing

Answer 39

in order for you to find an inverse, at least without restricting a domain, is to have a 1-1 function ... in which the f(a) = f(b) implies a=b would do the trick.

Answer 40

I am not sure how to make our function into that

Answer 41

f(x) = (x-1)/4 is a one to one function, and implies that f(a) = f(b) only iff a=b

Answer 42

so our function was already 1 to 1?

Answer 43

as defined, yes

Answer 44

So we finished? Or we have to find how to find the inverse?

Answer 45

since our function is 1-1, then by default, there is a unique y value for any given x value.

Answer 46

we find an inverse such that f(f'(x)) = x and f'(f(x)) = x

using our definition:

f(f'(x)) = (f'(x)-1)/4

x = (f'(x)-1)/4

4x = f'(x)-1

4x+1 = f'(x)

therefore: f(f'(x)) = (4x+1)/4 = x

does f'(f(x)) = x? try it out: 4(4-1)/4 + 1 = x

Answer 47

*** edit

... try it out: 4(x-1)/4 + 1 = x

Answer 48

Okay

Answer 49

then our inverse is f'(x) = 4x+1

Answer 50

I have to do the new one

Answer 51

not sure what a new one is ....

Answer 52

4(x-1)/4 + 1 = x equals all real numbers

Answer 53

f'(x) = 4x+1 is our inverse?

Answer 54

yes, and it shows that for any f(x) we can determine what x should be

spose f(x) = 5

5 = (x-1)/4, we can solve for x

Answer 55

yes: f'(x) = 4x + 1 would be the inverse of our defined f(x)

Answer 56

Thank you so much!

Answer 57

good luck with it all :)