Question

find the inverse of the function??

y=logbase4 x-2

Answer 1

@geerky42

Answer 2

is that \[y=\log_4(x-2) ~~or~~y=\log_4x-2\]

Answer 3

it has no parenthesis, but there is a space between the 4 and x

Answer 4

so it is the later.
since log is one-to-one we don't have any problem
we can go directly into finding the inverse function

Answer 5

how do we know if one to one? if we do f(g(x)) and (g(f(x)?

Answer 6

pretty good question
one to one means any element of domain maps to exactly one element of the range and the other way around

Answer 7

so if we take y=x^2
and try for example (-2) and 2 we see that both of them are giving 4
that means it is not one to one

Answer 8

Another way to tell if the function is one to one is by doing horizontal line test.

Answer 9

to speak clearly i should say one to one correspondence

Answer 10

yeah geometrically we can test this by a horizontal line like @geerky42 mentioned

Answer 11

if it passes horizontal test, it's one to one?

Answer 12

at any rate this not something new to you since you are dealing with inverse
the first and most important aspect to look at is this

Answer 13

yes!

Answer 14

that is what you were thought no?

Answer 15

i know that the logarithm of an exponental function is the inverse ? but how do i know this inverse of exponential?

Answer 16

well that is want we are going to find out!
and true log are inverse relation with exponential so
this one should give us some exp function of some sort

Answer 17

let's find out

Answer 18

first you switch the y and x roles
\[x=\log_4y-2\]
the game is to solve for y
so you need to have experience on solving such equation

Answer 19

how would you solve for y here?

Answer 20

well let me make it easier
\[x+2=\log_4y\]

Answer 21

any rule that come in mind to get rid of that log_4

Answer 22

meant "log base 4"

Answer 23

where are you leaving me behind ?

Answer 24

use change of base?

Answer 25

@xapproachesinfinity

Answer 26

nope

Answer 27

anything else?

Answer 28

go and check your notes lol

Answer 29

i really dont know??

Answer 30

it's equal to 4^x=y

Answer 31

how?

Answer 32

exponential form

Answer 33

where did you got that

Answer 34

well let me take you one step and you do the rest
\[x+2=\log_4y \Longrightarrow 4^{x+2}=4^{\log_4y}\]

Answer 35

oh

Answer 36

4^x+2 =y