Question

•Need help with 3 questions

•Need 2 Questions checked

•Will Medal & Fan!

Answer 1

@jim_thompson5910

Answer 2

Ok thanks, now what about the other 3? @jim_thompson5910

Answer 3

give it a shot and tell me what you get

Answer 4

or tell me how far you get with it

Answer 5

ooh that one about the linear function was tricky

Answer 6

i'd have said "sometimes true" also because \(f(x)=2\) does not have an inverse for example
but if you read carefully it does not say "inverse function" it says "inverse RELATION"

Answer 7

RIght, these are kinda tricky.

Answer 8

yeah the `relation` keyword makes me think it's always true because `y = 2` will have an inverse of `x = 2` which isn't a function, but it's a relation

Answer 9

Ok, lets move onto the three questions now..

Answer 10

how far did you get with #3 ?

Answer 11

ill say sometimes also on question about linear

Answer 12

do you agree that the original equation in #3 is a function? why or why not?

Answer 13

Ok Wait, are we talking about the one all the way at the bottom or the one at the top?

Answer 14

If we're talking about the question at the bottom, I say YES it is a function.

Answer 15

the one with celsius and fahrenheit

Answer 16

I'm thinking that's #3 since the first two were already done in another attachment

Answer 17

Ok I see, we're basically on #1

Answer 18

`If we're talking about the question at the bottom, I say YES it is a function.`

correct. The one with sqrt(x-4) is a function. But they aren't asking if it's a function or not for this one

Answer 19

yeah #1 if we're only focused on that attachment and forgetting everything else

Answer 20

Yeah

Answer 21

do you agree that the original equation in #1 is a function? why or why not?

Answer 22

Yes, Its a linear function.

Answer 23

why is it a linear function?

Answer 24

I found the degree of the equation lol

Answer 25

ok, another method is graphing and you'll notice a straight line forms

or you can notice it's in the form y = mx+b where m is the slope, b is the y intercept

m = 9/5
b = 32

Answer 26

which ever method you use, the end result is that the original function is linear. How about the inverse? Is the inverse a function?

Answer 27

Im not too sure on that part

Answer 28

isolate C to find the inverse

Answer 29

the inverse is not

Answer 30

why not?

Answer 31

I just took a guess just now, wasn't really sure..

Answer 32

what do you get when you solve for C?

Answer 33

\[- \frac{ 160 }{ 9 } + \frac{ 5F }{ 9 }\]

Answer 34

notice how it's in the form y = mx+b

now
m = 5/9
b = -160/9

Answer 35

so the inverse is linear and it's also a function

Answer 36

make sense?

Answer 37

Yeah I see the formula you used. Lets move on?

Answer 38

ok

Answer 39

okay #2

Answer 40

My teacher was going over this but this specific problem is tricky

Answer 41

what kind of function is f(x) ?

Answer 42

a linear equation

Answer 43

yep, and this rule is always true

if you have a nonconstant linear function, then it always has an inverse function

Answer 44

another rule

\[\Large (f \circ f^{-1})(x) = x\]

if the inverse function exists

Answer 45

ok

Answer 46

so this means

\[\Large (f \circ f^{-1})(-10) = -10\]

because the inverse does exist

Answer 47

most def! ok ok I see, lets move onto the last one..

Answer 48

what is the domain of f(x)?

Answer 49

hint: you cannot take the square root of a negative number

Answer 50

Domain:

Answer 51

correct

Answer 52

Rule: the domain of the original function will become the range of the inverse function

this is because x and y swap

Answer 53

so if the domain of f(x) is x >= 4, then the range of the inverse is x >= 4

Answer 54

Most Def

Answer 55

Thats what the range would be^

Answer 56

yes the range of f(x) is y >= 0

so the domain of the inverse is x >= 0

Answer 57

btw I meant to say

`so if the domain of f(x) is x >= 4, then the range of the inverse is y >= 4`

I changed the second `x>=4` to `y >= 4`

Answer 58

thanks for the help.