Question

Help Please!!! Begging you? I do not understand this and I really need help. Will fan and medal anybody who helps me (Algebra)

Answer 1

@TheSmartOne

Answer 2

Task 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
c
x
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 3

Part 1\[f(x) = x+a/b\] (to clarify all those numbers)
\[g(x)=cx-d\]

Answer 4

@Nnesha

Answer 5

what is f(g)?

Answer 6

f(x) = x + a/b

f(g) is just f composed of g, instead of composed of x

f(g) = g + a/b

but we have a definition for g, use it

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

now the thing is, what defines an inverse?

Answer 7

@amistre64 may we go part by part please?

Answer 8

i thought we did :)

lets start with what defines an inverse .... what can you tell me?

Answer 9

like f(g(x))=g(f(x))?

Answer 10

yeah, but somehtings missing

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

Answer 11

so lets set it up

what is f(g)? this is what i worked up to start with

cn work up g(f)? or ask me question if you get lost

Answer 12

ok i understand that is the inverse

Answer 13

So for part 1 i can put in any numbers right?

Answer 14

@amistre64

Answer 15

no, we are working it out to determine what numbers we can use.

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

what is g(f)?

Answer 16

g(f)=b/a+z-cx?

Answer 17

g(f) = c(f) - d ; replace f with its definition

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

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

not sure where z is coming from

Answer 18

ok thank you srry did not mean to put z (meant to pout d)

Answer 19

now since they have to equal x .... they have to equal each other at best

f(g) = g(f)

cx - d + a/b = cx + ca/b - d

since both side have a -d, it cancels out and can be anything it wants to be; whats your favorite d value?

Answer 20

idk 2?

Answer 21

2 is fine; let d=2

cx + a/b = cx + ca/b

now can you tell me, what c value we can use to make this true? give me an educated guess.

Answer 22

4?

Answer 23

4 might not be good

notice that if c=1

1(x) + a/b = 1(x) + 1(a/b)

Answer 24

ok so d=4 c=1

Answer 25

well, you said d=2 so lets not go chagning things ... d=4 is fine but it helps to stay consistent

Answer 26

now a and b can be anything you like, what makes your favorite fraction?

Answer 27

so d=2 c =1 fine
a = 3
b= 4

Answer 28

that should work like a charm

Answer 29

ok so lets fit it in may you do it please my mother is calling me

Answer 30

f(x) =3(1)-5
g(x)=1 +5/3

Answer 31

@amistre64 so part 1 is done

Answer 32

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

fill in the values

f(x) = x + (3)/(4)
g(x) = (1)x - (2)

now i have to see what we did wrong ..... since this didnt work out that well

Answer 33

ok thank you and we did nothing wrong :)

Answer 34

thats it tho, we cant do part 2 if part 1 isnt valid.

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

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

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

when c=1

x - d + a/b = x+a/b - d

this should be true for all abd values

but:

f(x) = x + 3/4 and g(x) = x - 2

are not inverses

so we would need to reevaluate the issue

let a/b = d ... or if b=1, then a=d

Answer 35

let a = d = 2, ;et c = b = 1

Answer 36

wait can you just show me the new equation please?

Answer 37

for part 1, because you are typing bad and it does not make sense

Answer 38

if working with me is incompatible, then you might what to find/wait for someone else. feel free to repost the question if you want so that others would be better attracted to it.

Answer 39

srry i did not mean to say in that kind of way i meant to say repost i also type bad i just kind of yeah.... @amistre64 please help me so let's con.?

Answer 40

@amistre64