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.

- horsegirl27

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- horsegirl27

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.

- horsegirl27

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

- horsegirl27

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

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## More answers

- horsegirl27

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.

- phi

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

- horsegirl27

yes.

- phi

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

- horsegirl27

For which part?

- phi

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

- phi

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

- horsegirl27

ok

- phi

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 ?

- phi

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

- phi

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

- horsegirl27

ok

- horsegirl27

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

- horsegirl27

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

- horsegirl27

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

- horsegirl27

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

- phi

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

- phi

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

- horsegirl27

yes. That's my work exactly.

- phi

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 ?

- horsegirl27

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.

- phi

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

- horsegirl27

oh, sorry

- horsegirl27

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

- phi

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

- phi

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

- horsegirl27

ok, that makes sense.

- horsegirl27

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

- phi

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.

- horsegirl27

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)

- phi

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)

- horsegirl27

ok, thanks.

- horsegirl27

By the way, any suggestions for an online graph?

- phi

I downloaded geogebra.

- horsegirl27

Okay, I'll download it too.

- horsegirl27

So, graph 5 points for each?

- phi

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

- phi

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

- horsegirl27

ok

- horsegirl27

Got it, thanks!

- horsegirl27

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

- phi

Here is the plot

##### 1 Attachment

- horsegirl27

thank you :D

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