Question

Please help me out!! I have work for the first part of this question, but then I'm confused. When reading it, it seems like parts 2 and 3 are the same, so I would like some clarification of what to do. For part 4, I'm not quite sure either....
Question posted below.

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).

Part 3. Show your work to evaluate g(f(x)).

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

Answer 2

I'm sorry, those functions are messed up, let me fix that.

Answer 3

f(x)=x+a/b
g(x)=cx-d

Answer 4

So, for part 1, I have f(x)=x+3/5 and g(x)=5x-3. I'm not sure of what I'm doing in parts 2 and 3.

Answer 5

is f(x)
\[ f(x) = \frac{x+a}{b} \]?

Answer 6

yes.

Answer 7

so we could write
\[ f(x) = \frac{1}{b} x + \frac{a}{b} \]

Answer 8

For which part?

Answer 9

just thinking out loud.

For part 2, they want you to show the functions are inverses.
start with your:
f(x)=(x+3)/5
g(x)= 5x-3

if they are inverses then f( g(x) ) = x

Answer 10

f( g(x) ) is short-hand for : everywhere you see "x" in the expression for f(x), erase the x and write g(x)

using
f(x)=(x+3)/5
g(x)= 5x-3

f( g(x) ) = ( g(x) +3 ) /5

Answer 11

ok

Answer 12

now we use g(x) = 5x-3 in
f( g(x) ) = ( g(x) +3 ) /5

in other words, on the right hand side, replace g(x) with its "definition" 5x-3
can you do that ?

Answer 13

you should get
\[ f( g(x) ) = \frac{( 5x-3 +3)}{5} \]

Answer 14

now simplify that.

For part 3, do almost the same thing
show g( f(x) ) = x

Answer 15

ok

Answer 16

And I am so sorry, I was gone for a moment.

Answer 17

Ok, so that's what I got for that part.

Answer 18

So for part 3, to I basically just solve it to show g( f(x) ) = x?

Answer 19

Because I worked it out and got it. Is that what I want to turn in for part 3, my work?

Answer 20

I assume for part 2, you got f( g(x))= x after simplifying?

Answer 21

\[ f( g(x) ) = \frac{( 5x-3 +3)}{5} = \frac{5x+0}{5} = \frac{5x}{5} = x \]

Answer 22

yes. That's my work exactly.

Answer 23

for part 3
g( f(x) )

start with
f(x)=(x+3)/5
g(x)= 5x-3

g(f(x)) means replace x in 5x-3 with f(x)
what do you get ?

Answer 24

g(f(x))=5(x+3/5)-3
Then the 3's will cancel each other out, and so will the 5's, to get g(f(x))=x.

Answer 25

you have to remember order of operations.
\[ g(f(x)) = 5 \cdot \frac{(x+3)}{5} -3 \]
multiply before add/subtract

Answer 26

oh, sorry

Answer 27

So then it will x+3/1 or 0? And then after that, the 3's will still cancel out, right?

Answer 28

the 5/5 becomes 1
and you get
\[ g(f(x)) = 5 \cdot \frac{(x+3)}{5} -3 \\ = 1\cdot (x+3) -3 \\=\ (x+3)-3 \\ =x+3-3 \\=x\]

Answer 29

just like
\[ \frac{15}{5} = \frac{5 \cdot 3 }{5} = \frac{5}{5} \cdot 3 = 1 \cdot 3 = 3\]

Answer 30

ok, that makes sense.

Answer 31

So for part 2, I'm showing for for f(x), and for part 3, showing work for g(x)?
Then graphing?
And I'm confused how I should graph this

Answer 32

Include a table of values for each function. Include 5 values for each function.

that means they want a table of x y values where y is f(x) or g(x) depending on which function you are doing.

Answer 33

ok, so for x I could use something like 0, 1, 2, 3, -1 and for y -3, 2, 7, 12, -8?
(i might not use those numbers, I just chose them randomly)

Answer 34

Start with the first function f(x)
f(x)=(x+3)/5

I would pick small negative and positive numbers for x to get integer answers for f(x) (i.e. y)

for example if you start at x= -8, and make x go up by 5 , you will get nice numbers for f(x)

Answer 35

ok, thanks.

Answer 36

By the way, any suggestions for an online graph?

Answer 37

I downloaded geogebra.

Answer 38

Okay, I'll download it too.

Answer 39

So, graph 5 points for each?

Answer 40

First write down the table

x | f(x)
--------
-8 | -1
-3 | 0

etc
and for g(x)
you can pick x= -2 to +2 by 1
x | g(x)
--------
-2 | -13
-1 | -8
etc

Answer 41

if you use geogebra
you type in
f(x)= (x+3)/5
and it will plot the line

Answer 42

ok

Answer 43

Got it, thanks!

Answer 44

I have one more question, want me to make a new thread?

Answer 45

Here is the plot

Answer 46

thank you :D