Question

I will give medal if someone can help me

Answer 1

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
f(x)= x+a/b




g(x)=cx−d


Part 2. Show your work to prove that the inverse of f(x) is g(x).

Answer 2

Do you know how to get the inverse of a function!?

Answer 3

Not exactly!

Here you are how to!

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function \(f^{-1}(x)\).

Answer 4

I just dont know how to do with a division or a fraction sign in it

Answer 5

I will walk with you step by step if you don't mind!

Answer 6

I would love that Im not good with functions but im a quick learner

Answer 7

Very nice, and that is with my pleasure!

Answer 8

A=6 B= 3

Answer 9

and for c and d?

Answer 10

Dont they need to be the same numbers

Answer 11

I will attach the file im working on to see what i mean

Answer 12

Ok. That would be better!

Answer 13

I got it. Then c and d will be ...?

Answer 14

C=6 and d=3

Answer 15

or is that backwards?

Answer 16

You mean c=3 and d=6!!
Don't you?

Yes, backwards!

Answer 17

Yes because is cx-d slope intercept form just like mx+b?
or is it something different

Answer 18

This is not the point!
Th point is b should be equal to c and a=d!

Answer 19

f(x)=x+6/3
g(x) = 3x-6

Answer 20

Yes, exactly like that!

Answer 21

that is part 1

Answer 22

So that is for Part 1, what about Part 2?

Answer 23

Part 2 is
F(x) = x+6/3
y=x+6/3
x=y+6/3
that is as far i got

Answer 24

so Do you face any difficulties with part 2?

Answer 25

That is part 2 there was nothing else like adding on both sides or anything with gx?

Answer 26

????

Answer 27

I thought there was more because that is to simple

Answer 28

So you would better to follow these steps:

To get the inverse of any function f(x) [ just make sure that it passes the horizontal line test] follow the steps:
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function \(f^{-1}(x)\).


I think the question asks for this!

Answer 29

So how did you get f^-1(x)

Answer 30

I see the steps but how would I do that in numbers

Answer 31

Start with f(x).
Show me your works please

Answer 32

f(x) = x+6/3
then you would switch the fx into a y
y = x+6/3
then switch y with x and x with y
x = y + 6/3
That is all I know for now

Answer 33

Not quite correct!

Here is the right order of steps:

\[\LARGE f(x) = \frac{ x+6 }{ 3 }\]
switch the f(x) into y:
\[\LARGE y = \frac{ x+6 }{ 3 }\]
Solve for x:
\[\LARGE 3*y = x+6 \]
\[\LARGE 3y -6= x\]
\[\Huge\color{Coral} x=3\color{Aqua }y -6\]
Swap x and y:
\[\Huge\color{Aqua } y=3\color{Coral}x -6\]
\(g(x)\) is the inverse of \(f(x)\):
\[\Huge\color{Aqua } g(x)=3\color{Coral}x -6\]

Answer 34

sorry i was in the bathroom

Answer 35

yes i get it now but how would I graph this because I am so bad at graphing

Answer 36

It's nothing.
Did you get the idea?

Answer 37

Graph f(x) or g(x)?

Answer 38

how would i graph when im on word document?

Answer 39

I have to graph both

Answer 40

So Take a look at that site. It is cool and interesting!
I think this would help you.
https://www.desmos.com/calculator

Answer 41

would it look like that i never used this website before

Answer 42

Is this g or f?

Answer 43

f

Answer 44

i will show you g if this is correct because i do not know how to use this website

Answer 45

https://www.desmos.com/calculator/iclr12gm2j

Answer 46

That is what i put so yes i got right i will show you g

Answer 47

Ok.

Answer 48

(0,-6) - (2,0)
draw a line through those points
am i right?

Answer 49

about g(x) you are talking?

Answer 50

yes

Answer 51

i will be working out the other problems on this file and can you tell me if I am on the right track?

Answer 52

SO this one firstly: Are you persuaded?

Answer 53

About this first part then yes this was a big help

Answer 54

i am