Monday, March 27, 2023
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#1
 abrowaqas Junior Member Join Date: Jun 2006 Location: Hyderabad Pak Posts: 26 Thanks: 44 Thanked 14 Times in 10 Posts  Pure Maths

Always we have given the COMPOSITE FUNCTIONS in that format i-e

f= something
g= something

and then we have to find "fog" and "gof" .....

but never in any book .. . composite functions are given then we have to find original functions...... i -e

fog= something
gof= something

f=??
g=??

(((AWA)))
#2
 elementofsurprize Member Join Date: May 2006 Posts: 54 Thanks: 0 Thanked 1 Time in 1 Post  One Approach

Now, we easily conclude: Dom(g(f(x))=Dom(f(x))
Range(g(f(x))=Range(g(y)) (assuming that g is defined over y)

Keeping this in mind we can arbitrarily make two functions out of the given g(f(x)) function so that all the variables are grouped in one function which we will call f(x) and the whole will be g(f(x)).

For example: Given: g(f(x))=3x^2-2x-9. (^ stands for power)
We can arbitrarily say, f(x)=3x^2-2x. So g(y)=y-9#

Now, if we are given some conditions regarding the functions f or g then we can't break g(f(x)) arbitratily. We have to break it in a way that the conditions for f and g are also satisfied.

I hope this helps you. If there are questions then I am interested too.
__________________
Smyler wyth nyfe undur the cloke
#3
 Ashher Junior Member Join Date: Jul 2006 Posts: 1 Thanks: 0 Thanked 1 Time in 1 Post  Composition functions

MR. ElementOf surprise!
u have written a thing which is mathematically incorrect.
i.e.
if g(f(x)) = something ...that does not imply that dom (g (f(x)) = dom (f(x)).
Consider the following counter example.....
Let f(x) = x^2. then Dom (g(f(x)) = postive real numbers and zero...however dom(f(x)) = All real numbers.
 The Following User Says Thank You to Ashher For This Useful Post: Ambreen Nasir (Saturday, October 10, 2009)

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