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Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is
( f o g ) ( x ) = f ( g ( x ))
In other terms, compositions are evaluated by plugging the second function listed in the first function listed. Note that order is significant here. Usually interchanging the order will result in a different answer.
Example Given f ( x ) = 3x2 - x = 10 and g ( x ) = 1 - 20 x determine each of the following.
(a) (f o g ) (5)
(b) ( f o g ) ( x )
Solution
(a) (f o g) (5)
In this case we've got a number rather than an x but it works in precisely the same way.
( f o g ) (5) = f (g (5))
= f ( -99) = 29512
= f (1 - 20x )
= 3(1 - 20x )2 - (1 - 20 x ) + 10
= 3(1 - 40x + 400 x2 ) -1 + 20 x + 10
= 1200 x2 -100 x + 12
Compare this answer to the next part & notice that answers are NOT the similar. The order wherein the functions are listed is important!
Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?
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y=3x^2+12+11
korda ab e ndan rrethin me qender o ne dy harqe njeri prej tyre eshte sa trefishi i tjetrit gjeni masat e harqeve dhe masat e trekendeshit aob
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