Question

Can someone help me please
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

can someone help me please

Answer 2

You should pick simple numbers for a and b

Answer 3

a is 6 and b is 9

Answer 4

by the way is it
\[ f(x) = x + \frac{a}{b} \]
or
\[ f(x) = \frac{x+a}{b} \]

Answer 5

also, life is a bit easier if you use *small numbers* like 1 and 2!

Answer 6

we could use the second one

Answer 7

sure

Answer 8

It makes a difference to the answer. can you use the equation editor to post the exact equations for f(x) and g(x) ? otherwise, we do a lot of work and get the wrong answer.

Answer 9

f(x)=x+1/2

Answer 10

and is that x plus one-half

or (x+1) all divided by 2 ?

Answer 11

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

Answer 12

\[g(x)=cx-d\]

Answer 13

ok, so you should write it as
f(x) = (x+1)/2

to find the inverse, rename f(x) as y
y= (x+1)/2 (and remember this , because they want you to plot this line)

next, "swap the x and y"
can you do that ?

Answer 14

swap means erase the "y" and put x in its place
then erase the original "x" and put in y

what do you get ?

Answer 15

y=1/2+1 i guess

Answer 16

start with
y= (x+1)/2

change the first "y" into x
what do you get ?

Answer 17

Is this the segment honors project?

Answer 18

yes

Answer 19

then in the (x+1) change that "x" into a y

Answer 20

i confused

Answer 21

the procedure to find the inverse has a few steps
the first step is to "rename" x to y and the y to x
there is no thinking involved. If you see y, write x, if you see x write y
start with
y = (x+1)/2

Answer 22

and leave all the other "stuff" as it is

Answer 23

x=(y+1)/2

Answer 24

yes

Answer 25

the next step is "solve for y"

I would start by multiplying both sides by 2
that means write *2 on both sides (that means times 2)

Answer 26

x(y+1)/4

Answer 27

it is clearer if you write it like this
\[ x = \frac{y+1}{2} \\ 2\cdot x = 2\cdot \frac{y+1}{2} \]

Answer 28

in algebra we don't usually show the multiply sign when we do number times letter
we would write 2*x as just 2x

Answer 29

on the right side you have a 2 "up top" and a 2 "down below"
that means you have
\[ \frac{2}{2} \]
do you know what that simplifies to ?

Answer 30

1

Answer 31

yes, so the right side is the same as 1*(y+1)
which is just (y+1)
so far you have
\[ 2x= (y+1)\]
the parens are not doing anything so it is the same as
\[ 2x = y+1 \]
or
\[ y+1= 2x \]

Answer 32

next, write -1 on both sides
what do you get ?

Answer 33

2(1)=1+1

Answer 34

start with
y+1 = 2x

write -1 on each side
don't do anything else. what does it look like?

Answer 35

1+1=2x

Answer 36

1+=2(1)

Answer 37

no, we leave the y alone
you have
y+1 = 2x

now write -1 on both sides, like this
y+1 -1 = 2x -1

Answer 38

on the left side you have 1 take away 1

Answer 39

1 -1 is 0
y+0 is y (adding 0 does not do anything)
you're answer is
y= 2x-1

the last step is rename y to be g(x)

Answer 40

g(x)= 2x - 1

now you know what 'c" and "d" are, by matching your answer with
g(x)= cx - d

Answer 41

thanks you so much phi