Question

The composition functions f?g and g?f are equal to each other for any f and g.

This isnt true, right? My only question is what is a "composite function"

example:
f=x-1
g=x^2
f(g(x))=x^2-1
g(f(x))=x^2 -2x +1

Answer 1

A composite function is a function made up of 2 functions. You "do" g(x) to f(x) here to find the result.

Answer 2

g(f(x)) should be (x-1)^2 instead

Answer 3

(x-1)(x-1)
x^2-x
x^2-x-x
x^2-x-x+1
x^2 -2x +1
i wrote it correctly i believe

Answer 4

soooo this is false?

Answer 5

the statement " f?g and g?f are equal to each other for any f and g." is false

Answer 6

thanks:)

Answer 7

f=x-1
g=x^2
f(g(x))=x^2-1
g(f(x))=(x-1)^2 = x^2 -2x +1

Answer 8

yes your x^2 -2x +1 is correct too

Answer 9

the reason why it is false it is because it says 'for any f,g f compose g = g compose f' . This is not true generally (it is true when f and g are inverses of each other) .
So all you have to do is find a counterexample. and you found a counterexample

Answer 10

To falsify a general statement such as above , it is sufficient to find one counterexample.

Answer 11

@perl do you know which function is the reflection on y=x ?

Answer 12

inverse function is reflection on y=x right ?

Answer 13

the inverse function , i think

Answer 14

ok thanks!

Answer 15

it is not necessarily a function, to flip x and y . sometimes we just call it the 'inverse relation'

Answer 16

for example if you reflect y = x^2 about the line y = x , you don't get a function

Answer 17

@perl can you take a look at my product moment coefficient qn ?