Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

16 Introduction to Analysts [Ch. 1
42. Write as a single equation the composite functions represented
as a series of equalities:
a) y = u*> w = sin#;
b) # = arctan, u = Yv, y = log#;
w, if t/0;
*_!.
43. Write, explicitly, functions of y defined by the equations:
a) x2 arc cos y = n;
b) 10* +10' =10;
c) * + \y\ = 2y.
Find the domains of definition of the given implicit functions.
Sec, 2. Graphs of Elementary Functions
Graphs of functions # = /(*) are mainly constructed by marking
a suffi-
ciently dense net of points Ai /(*,-, //), where */, = / (*,-) (/ = 0, 1, 2, ...) and
by connecting the points with a line that takes account of intermediate points.
Calculations are best done by a slide rule.
Fig. 3
Graphs of the basic elementary functions (see Ap pendix VI) are readily
learned through their construction. Proceeding from the graph of
y = f(x), (T)
we get the graphs of the following functions by means of simple geometric
constructions:
1) 0i = M*) js th * mirror image of the graph T about the *-axis;
2) 0i=/( *) is the mirror image of the graph F about the #-axis;