Question

@phi can you walk me through this

Answer 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)=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 2

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

Answer 3

u know how to find inverse??

Answer 4

No i don't someone tried to explain but I still don't understand they said switch x with y

Answer 5

okk thn follow

Answer 6

interchange x and f(x)

Answer 7

these are steps to find inverse ...so replace n tell what u got ??

Answer 8

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

Answer 9

step 2: now replace f(x) by f ^-1 (x)

Answer 10

\[x=\frac{ f ^{-1}(x)+a }{ b }\]

Answer 11

for convenience let f^-1 (x) = y itzz not a step but just for convenience

Answer 12

\[x=\frac{ y+a }{ b }\]

Answer 13

now we need to take a & b from right side

Answer 14

multiply both side by b ...what u got ??

Answer 15

u there ??

Answer 16

sorry froze up

Answer 17

\[bx-a=y\]

Answer 18

@gorv

Answer 19

that is our inverse

Answer 20

before we proceed tell me u got how to find inverse ??

Answer 21

will we be using g(x)? noticed we didnt touch that

Answer 22

yes change y with x or f(x) with x

Answer 23

so Q says f(x) and g(x) are inverse
so find f inverse

Answer 24

so f inverse = g

Answer 25

ok and to show that i solve for y for f(x)?

Answer 26

y is our inverse
y=f^-1(x) replace y with it
and show the steps in your notebook

Answer 27

now compare f inverse and g

Answer 28

\[x=\frac{ y+a }{ b }\]
\[bx-a=y\]
similar to the g(x)
g(x)=cx-d

Answer 29

yeah and equate both inverse after that