Question

Consider the function f(x) = 1/3x+ 2
Use function composition to show that f(x) and g(x) are inverses of each other.

Answer 1

where is g(x) ?
or u need to find it ?

Answer 2

need to find it. @hartnn

Answer 3

so let y= 1/3x+2
exchange x and y
x=1/3y+2
can u find y in terms of x now ?

Answer 4

is it 3x-6?

Answer 5

@hartnn

Answer 6

yes. that is g(x).
now find f(g(x))

Answer 7

1/3 (3x-6)+2 = x-2+2=x ? @hartnn

Answer 8

or is it 1/3(3x-6)+2=3(1/3x+2)-6 ?

Answer 9

good work :)
since f(g(x))=x
u have verified that f and g are inverse of each other.
also prove that g(f(x)) = x

Answer 10

wait which one was correct? the first one i said or the second. ?

Answer 11

first.

Answer 12

ok. so now how do i graph this?

Answer 13

I have to draw the graphs of f(x) and g(x) on the same coordinate plane.

Answer 14

f(x)=y=1/3x+2
put x=0, y=?
put y=0,x=?

Answer 15

put x = 0, y= 1/3?

Answer 16

Im not sure... @hartnn

Answer 17

put x=0
y=1/3 x + 2
y=0+2
y=2.
ok?

Answer 18

ok so 0,2? and 0,-6?

Answer 19

those are the coordinates?

Answer 20

0,2 is correct
(-6,0)

Answer 21

ok so (0,2) and (-6,0)

Answer 22

i draw this on the x-axis? or y axis?

Answer 23

yup, plot those points. and join them by straight line..

Answer 24

(0,2) will lie on y axis.
(-6,0) will lie on x-axis

Answer 25

the -6 gets a closed circle and the 2 is open right?

Answer 26

circle ?

Answer 27

never mind. that's for a different one :D THANKS FOR YOUR HELP!

Answer 28

how do i eXPLAINE how my grapgh shows that the functions are inverses of each other?

Answer 29

sorry for late reply.
u can verify that f and g are inverses of each other by seeing that when f is reflected over line y=x , we get g.
here's the plots:
http://www.wolframalpha.com/input/?i=plot+x%2F3%2B2++and+3x-6+and+x

Answer 30

u asked same question @lavalava
did u get all 3 parts ?

Answer 31

@Riza still any doubts ?

Answer 32

@hartnn no sir thanks