Question

Create a function, consisting of two different operations. Prove that your function is a legitimate function. Using your function, explain to how to solve for f(3). Show your work and explain each step using complete sentences. Also, explain how to find the inverse of your function

Answer 1

write down any math statement with addition and multiplication

Answer 2

then put f(x) = in front of it

Answer 3

f(x)=6x-9=4x+7

Answer 4

well only one =

Answer 5

so f(x) = 6x-9

Answer 6

this is a function from R to R, you can prove its a function by checking two properties

1) f(a) is defined for all a in R...this is true because you can put any real number as an input to this function

2) a=b implies f(a) = f(b) you can prove this by starting with the assumption a=b

then multiply both sides by 6

6a=6b then subtract 9 from both sides

6a-9 = 6b-9 in other words f(a) = f(b)

so our "thing" is indeed a function.

can you find f(3)?

Answer 7

Ok, but I need two different operations

Answer 8

6*x+(-9)

Answer 9

that is two

Answer 10

multiplication and addition

Answer 11

No, what I mean is on operation on one side and another operation on the other side.

Answer 12

that is not what its asking

Answer 13

f(x) will always be by itself on one side.....

Answer 14

A math statement is something WIHTOUT a = sign
A math equation is something with an = sign
A function is f(x) = something

Answer 15

Oh okay, I understand

Answer 16

So how can I prove its f(x) = 6x-9 a legitimate function?

Answer 17

I showed you \(\uparrow\)

Answer 18

Oh, okay. So I just plug in three for the f(3) part, and how about inverse?

Answer 19

to find the inverse, switch the x, and y then solve for y

\(y=6x-9 \) becomes \(x=6y-9\) solve for y

Answer 20

\(y=\frac{x+9}{6}\)

Answer 21

so \(f^{-1}(x) = \frac{x+9}{6}\)

Answer 22

How could I solve this?

Answer 23

\(x=6x-9\iff x+9=6y\iff \frac{x+9}{6}=y=f^{-1}(x)\)

Answer 24

Do I have to find for either variables?

Answer 25

im confused by the question

Answer 26

So my function is f(x)=6x-9
Solving for f(3) is f(3)=6(3)-9
And the inverse is what you wrote above.

Answer 27

correct

Answer 28

For my answer I'd write exactly what you wrote?

Answer 29

For the inverse?

Answer 30

yes that would work, but I fear you are not understanding it all.. please ask if you have any questions.

The reason I say this, is because when someone asks " so thats what I put as the answer" usually means they are not even sure what the question is asking ( what is a inverse of a function ).