Question

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 1

plz help

Answer 2

@zepdrix

Answer 3

@undeadknight26

Answer 4

plz help

Answer 5

@Here_to_Help15

Answer 6

will fan you if i know how to

Answer 7

will fan you

Answer 8

plz help me

Answer 9

help

Answer 10

Ok

Answer 11

thx

Answer 12

@Here_to_Help15 are you there

Answer 13

We want f(x) and g(x) to be inverse functions of each other. In general, if you want to find the inverse function, rearrange the equation so that you solve for x, instead of f(x), then make every x an f(x) and make every f(x) an x (i.e. switch the variables). What you're left with is the inverse of what you started with.

So...choose any two numbers you want for a and b, then rearrange the equation as I described above. Look at your new equation, and if you put it in the same form as g(x) above, you'll see what c and d are right away!

Answer 14

ok

Answer 15

you mean like x=f(x)+ab

Answer 16

\[f(x)=x+a/b\]

Answer 17

hello

Answer 18

I mean solve for the other variable, THEN switch.

So if you're starting with:

\[f(x)=x+{a \over b}\]
Solving for x instead of f(x) gives you:
\[x=f(x)-{a \over b}\]
But this is still the same FUNCTION as you started with, because all you did was rearrange the terms. Your INVERSE function will be in the same form, but with x and f(x) switched - this creates a new function because you have changed the relationship between x and f(x):
\[f^{-1}(x)=x-{a \over b}\]

Answer 19

ok thx

Answer 20

can you help me with another parts too

Answer 21

\[f(x)=(x+a)/b\]

Answer 22

the equation wasn't f(x)=x+a/b

Answer 23

it was the whole x+a /b

Answer 24

Ah gotcha

Well same process for that function. What is the inverse of that?

Answer 25

x=(f(x)+a)/b?

Answer 26

and sorry about this mess i am new to this program

Answer 27

That's ok!

So yes, that would be the inverse function, but now isolate f(x) so that it's alone on the left side of the equation. What do you get?

Answer 28

is it f(x) = x/b +a/b

Answer 29

hold on

Answer 30

\[(x+a)/b=f(x)?\]

Answer 31

Not quite. Look:

\[x= {f(x)+a \over b}\]\[x \times b = {f(x)+a \over b} \times b\]\[bx= f(x)+a \]\[bx-a= f(x)+a -a\]\[f(x)=bx-a \]
So this is our inverse function. The question calls this g(x), with variables c and d. Looking at this new equation, what does c equal and what does d equal?

Answer 32

yes

Answer 33

i think so

Answer 34

matt101 you there?

Answer 35

Yes I am - just waiting for you to answer my question!

Answer 36

i said yes i think so

Answer 37

yes it does equal c and d

Answer 38

matt101 you there

Answer 39

matt 101 you there?

Answer 40

@matt101

Answer 41

hello anyone?

Answer 42

matt 101 are you there

Answer 43

Yup sorry just stepped away for a second.

So what exactly does c equal?
And what exactly does d equal?

Answer 44

sorry i was off too

Answer 45

c is the y-intercept and d is slope?

Answer 46

you there matt101

Answer 47

Well it's the other way around actually...

But I was referring to the actual values of c and d. Have a look at the inverse function I got above, and what they give as g(x) in the question:

f(x)=bx-a
g(x)=cx-d

Soooo what does c equal and what does d equal?

Answer 48

c is y-intercept and d is slope?

Answer 49

What I'm trying to get you to say is that c=b and d=a.

Look at the two equations I wrote above. And by the way, when you have an equation in y=mx+b form, the m is the slope (in this case c) and the b is the y-intercept (in this case d).

Answer 50

so sorry i am confused

Answer 51

ok

Answer 52

matt101 you there

Answer 53

Yes. What don't you understand?

Answer 54

oh never mind now i get it

Answer 55

that is it for part A b,c,d

Answer 56

Well no, for part A you need numbers for a, b, c, and d.

Choose any two numbers you want. You only need two because a=d and b=c.

For part B, write in these numbers instead of a, b, c, and d, and find the inverse of f(x) to show that it's equal to g(x)

Answer 57

how about 5 and 2

Answer 58

Sure

Answer 59

which means we have to insert it for c and d

Answer 60

Right

Answer 61

which means that is it for part 1 and part 2

Answer 62

Yes. Now for part C - you need to find g(f(x)). That means in g(x), you need to sub in f(x) for every x.

Answer 63

what did mean by you need to sub in f(x) for every x i didn't get that

Answer 64

do you mean g(f(x))

Answer 65

Yes.

g(x)=cx-d

Or in your case,

g(x) = 5x-2

Now,

g(f(x))=5f(x)-2

We know f(x)=(x+2)/5, so our equation then becomes:

g(f(x))=5((x+2)/5)-2

So I've pretty much given you the answer for part C now lol

Answer 66

But you can simplify that last equation just a bit further...and you might be surprised at what you get!

Answer 67

ok

Answer 68

is it g(f(x))=x

Answer 69

Absolutely right!

Answer 70

That's it for part C. For the last part you just need to graph f(x) and g(x) and the line y=x.

Come up with a table of values for each to make them easy to plot!

Answer 71

hold on

Answer 72

so basically we are just making a table out of random choice of ordered pairs in x and y

Answer 73

Yup

Answer 74

domain means x right?

Answer 75

domain: 5,6,9,4,8
range: 1,4,3,2,7

Answer 76

is it like that

Answer 77

For which function?

Answer 78

g(x)?

Answer 79

If you plug in x=5 to g(x) what do you get?

Answer 80

g(5)?

Answer 81

Yes what is g(5)?

Answer 82

i am confused at part d

Answer 83

You're just graphing the functions the way you would for any other.

If you sub 5 into g(x)=5x-2 what do you get?

Answer 84

i am weak at algebra

Answer 85

g(5)=5(5)-2
g(5)=?

Answer 86

g(5)=25-2
g(5)=23

Answer 87

Right! That's one point on your graph for g(x) - (5,23).

Now repeat the process for 4 other values of x. Use the 5 points to draw the line.

Then do the same for f(x), and once more for y=x.

Answer 88

oh now i get it

Answer 89

Great! Glad I could help :)

Answer 90

g(6)=28

Answer 91

g(9)=43

Answer 92

g(4)=18

Answer 93

g(8)=38

Answer 94

is it correct?

Answer 95

Yup

Answer 96

now the ordered pair for g(6) would look like this (6,28)

Answer 97

@matt101