Question

Match the function (f) with its inverse (f-1).
f(x) = x+6/2
f(x)= 1/3x + 4
f(x)=3x + 3
f(x)=7*8-4/8
f(x)= 3x + 1
Please help me!

Answer 1

Pardon me, which is the original function you are talking about?

Answer 2

They are all original functions..

Answer 3

I need the inverse for them all

Answer 4

oh, I understand, I thought this is a list of solutions where you can pick one, so if I understand this question correct - excuse me, but nowadays I have to double check - you have to find the inverse function to each of them?

Answer 5

Ok, so lets do one together then.

Answer 6

Ok thanks

Answer 7

The first one, doesn't really matter which one we do, they are all linear and therefore bijective.

\[y=x+\frac{6}{2} \]
First you want to solve for x and represent it as a function of y.

\[ x = \frac{2y-6}{2} =y-3\]

Answer 8

Did I read the first equation correct? or is it everything divided by two?

Answer 9

\[y= \frac{x+6}{2} \neq x+3 \] (-:

Answer 10

Thats correct

Answer 11

No sorry its all divided by 2

Answer 12

I said the inverse is 2x-6 is that correct?

Answer 13

good
so again, but same procedure, you always do it the same way, solve for x. So you will get
\[ x= 2y-6 \]

Answer 14

Ok good

Answer 15

Exactly, at this step you just 'switch' the variables, so you represent the inverse function as a function of x again rather then a function of y and you will get

\[ y=2x-6\]

Answer 16

and that's what you will have to do for all of them, good exercise anyhow.

Answer 17

Im confused on the next one

Answer 18

is the x in the denominator? or in the numerator?

Answer 19

Its being multiplied

Answer 20

\[y = \frac{1}{3} x+4\] like this?

Answer 21

yes

Answer 22

Ok this means it's in the numerator.

\[ y = \frac{1}{3}x+4 = \frac{x}{3}+4\] rules of multiplication

Answer 23

I said its 3x-12

Answer 24

correct

Answer 25

so would the third one be the same, 3x-12 also?

Answer 26

\[ y=3x+3\]
\[ x= \frac{1}{3} (y-3) \]

Answer 27

\[y= \frac{1}{3}(x-3)\]

Answer 28

so what does that mean?

Answer 29

that means that the inverse of the third function is what I just posted.

Answer 30

you asked if it's 3x-12 also, it is not.

Answer 31

Functions and inverses are something unique in that case, so different functions never share the same inverse.

Answer 32

ok... is the fourth?

Answer 33

the forth looks like you are missing an x term, if not then it is only a number, therefore a constant function, a constant has no inverse.

Answer 34

ok thanks

Answer 35

you're welcome