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It is not continuous at x= 0 Theorem 2 Suppose both f(x) and g(x) are continuous at x= a Then (a) f g, f g, and fgare continuous at x= a (b) If g(a) 6= 0, then f=gis continuous at x= a Theorem 3 If fis continuous at a, and if gis continuous at f(a), then f g is continuous at a Intermediate Value Theorem (IVT) Suppose fis continuous onDepartment of Computer Science and Engineering University of Nevada, Reno Reno, NV 557 Email Qipingataolcom Website wwwcseunredu/~yanq I came to the US< 9 8 ;
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CLAY DARKSTALKER DRAGONET ICEWINGS MUDWINGS NIGHTWINGSOtherwise, if f gand gis bounded from above, then f(x) g(x) sup A g for every x2A Thus, fis bounded from above by sup A g, so sup A f sup A g Similarly, f g implies that sup A( f) sup A ( g), so inf f inf g Note that f gdoes not imply that sup Af inf g;Note that (f B g)(x) ≠ (g B f)(x) This means that, unlike multiplication or addition, composition of functions is not a commutative operation The following example will demonstrate how to evaluate a composition for a given value Example 6 Find (f B g)(3) and (g B f)(3) if f ( x ) = x 2 and g ( x ) = 4 – x2 Solution Step 1 Find (f
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