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kymber
 3 years ago
Composition of functions?
kymber
 3 years ago
Composition of functions?

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ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4I think that this is pretty easy for you. We know,\[(g \circ f)(x) = g(f(x)) \]Therefore, our composition simplifies as the following:\[(g \circ f)(x) \implies g(f(x)) \implies g(2x  1) \implies (2x  1) +2 \]

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Do you get the above?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4... or should I be more informal? lol

kymber
 3 years ago
Best ResponseYou've already chosen the best response.3I don't understand what composition means :I

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Never mind that "composition" word. lol

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Do you still understand my explanation?

kymber
 3 years ago
Best ResponseYou've already chosen the best response.3No. I don't understand what I'm supposed to be doing at all! :'(

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4I'd give you an example.\[\sqrt{x + 1} \]We're doing two things to \(x\). First, we are finding the square root of x, then we are adding 1 to x. So,\[x + 1\]is the composition of two functions: \(\sqrt{\text{stuff}}\) and \(\text{stuff} + 1\).

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Here, we are again doing two things to \(x\). First, we are multiplying two to it and adding 1(which is \(2x  1\)) Then, we are adding two to that number.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4Operation Multiply Two And Subtract 1 got a boring name, which is f(x). Operation Add Two To Whatever Comes In Our Way got the name g(x).

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4\(x\) went to Operation Multiply Two And Subtract 1, and then became \(2x  1\). Sad :(

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.4And then it went to Operation Add Two To Whatever Comes In Our Way and became \(2x  1 + 2 = 2x + 1\)
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