6. f X, f - Y f (X) Y.
f (x) = y 0, | (6.40) |
g (y) = z 0, | (6.41) |
x x 0 ( ) g[ f (x)],
g[ f (x)] = g (y). | (6.42) |
xn x 0, xn X, n = 1, 2,...; (6.40)
yn f (xn) y 0, yn Y, n = 1, 2,...
(6.41) g (yn) z 0, yn = f (xn), , g[ f (x)] z 0, n = 1, 2,..., . . (6.42).
1. Y y 0, . .
g (y) = g (y 0), | (6.43) |
(6.42)
g[ f (x)] = g ( f (x)). | (6.44) |
, . , 6
g[ f (x)] | = | g (y) | = | g (y 0) | = | g ( f (x)). |
(6.42) | (6.43) | (6.40) |
, , , :
. f x 0, g y 0 = f (x 0), g f x 0.
, f x 0 ,
f (x) = f (x 0) = y 0, | (6.45) |
g y 0 (6.44)
g[ f (x)] | = | g [ f (x)] | = | g f (x 0) |
(6.44) | (6.45) |
.. g f x 0.
2. , , , , , .
, f(x) a∈R (R− ), {xn}, , limn→∞xn=a, limn→∞f(xn)=f(a). 3 f(x) x=a ( ):
7 ( ).
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