Question

FAN AND MEDAL PLEASE HELP

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).
@ganeshie8 @amistre64 @uri

Answer 1

btw its g(x)=cx-d

Answer 2

lets start with how do you define an inverse?

Answer 3

I think it is an opposite

Answer 4

an inverse undoes .... is a good way to look at it, but more mathically:

if f and g are inverses then:

f(g(x)) = x AND g(f(x)) = x

for all x

Answer 5

but it says to insert numbers for them and then explain how they are inverses i just dont understand this lesson at all.

Answer 6

well, we need to determine what values will make them inverses; so lets start by making the compositions and then see where it leads us

Answer 7

okay

Answer 8

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

Answer 9

the first one

Answer 10

then f(g) = (g+a)/b = (cx-d+a)/b is an inverse at best if f(g) = x

and g(f) = cf-d = c(x+a)/b - d is an inverse at best if g(f) = x

since x=x, when does:

(cx-d+a)/b = c(x+a)/b - d

Answer 11

or we might be able to work it simpler one by one

c(x+a)/b - d = x

and

(cx-d+a)/b = x

either way we should be able to get some options worked out for us

Answer 12

okay so now we plug in numbers?

Answer 13

we can start plugging numbers sure, like b=1 might be a good start

Answer 14

so now its c(x+a)/1-d=x and (cx-d)/1=x

Answer 15

or work it all out such that

(cx-d+a)/b = c(x+a)/b - d

cx-d+a = c(x+a) - bd

cx-d+a = cx+ca - bd

-d+a = ca - bd

Answer 16

so nvm its -d+a=ca-1d?

Answer 17

well, from this, if we let b=1 and c=1

a-d = 1a - 1d is true for any values of a and d

Answer 18

oh okay so is that the answer for part 1 and 2

Answer 19

well, part 1 says to find some abcd values that make f and g inverses.

part 2 says to prove that those values work

Answer 20

show that f(g) = x and g(f) = x for c=1, b=1, a=a, d=d

Answer 21

okay

Answer 22

of course pick your favorite a and d values since they seem to be unimportant overall

Answer 23

6

Answer 24

so a=6, and d=?

Answer 25

4

Answer 26

that should work fine :)

Answer 27

so:

f = (x+6)/1, g=1x-4

f(g) = (x-4)+6 doesnt equal x so we might have to try this again. might be a typo up there

Answer 28

what do you mean?

Answer 29

Dang it i have to go in like 30 mins

Answer 30

f = (x+a)/b

g = cx - d
----------------------

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

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

inverses are defined as:

f(g) = x
g(f) = x

(cx-d+a)/b = x
c(x+a)/b - d = x


cx +a -d = bx
cx +ca - bd = bx

let b=1

cx +a -d = x
cx +ca - d = x

let c=1

x +a - d = x
x +a - d = x

a-d = 0 if a=d is where we went wrong

Answer 31

if a=6, then d=6

Answer 32

the process of determining abcd is actually proves they are inverses, but they seem to want you to go about it in a backwards kind of way.