Composite Functions

[silk solar]

Help composite functions is messing me up

[forest depot]

<@&1227988399579730072>

Note for OP

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[wraith magnet]

For the first one, write it as f(|x|)+|f(x)|. And then caseworking or graphical approach would give you the graph of h(x).

[silk solar]

yahi to nahi hota na ji

please explain kaise karrte hai ye

2-3 hafte se nahi kara to bhul gaya hu ab

[wraith magnet]

Wait Imma try and find a pen and paper

[silk solar]

thenkuu

[wraith magnet]

My apologies for the poor quality of graphs, but it would be something like this 😭

[silk solar]

oooooooooooo ok so how do define the functions tho

thats also something i forget at times like

the process of defining it

fog and gof

[wraith magnet]

fog (sounds like f o' (of) g) is f of g which is f(g(x))

[silk solar]

how wll we define gof here

[molten wasp]

Hello.

[silk solar]

yoyo hepl

[wraith magnet]

In this case, g(x) is modulus function

[molten wasp]

g(f(x)) = |f(x)|

Wherever there's an x, replace it with a f(x)

Then sub in your f(x) with the necessary boundary conditions

[wraith magnet]

Sorry for the delay, but the questions and graphs would look something like this.

Or you could have also defined the fog and gof over various intervals and then added them to get the result.

[teal chasm]

you good?

[silk solar]

ooooo yea im done wth this i forgor about this hehe

+solved @wraith magnet