12.1.
Otherwise, the trig functions would not be monotonic.
It implies that trig functions may take the same
values for different arguments. In turn, it means
that the inverse functions may have more than
one value for one argument. It contradicts to
the definition of a function.
12.2.
a). Here one value on horizontal
axis may correspond to more than one value on
vertical axis.
12.3.
12.4.
On the segment [0, 1], this function is inverse
to itself.
12.5.
b). The inverse function is the
image of the original function over the line y
= x.
12.6.
x
0. It is the interval (– ,
0].
12.7
arcos x has the range [0, 180°]. Therefore,
1) arcos 0.93 = 21°
2) arcos 0.24 = 76°
3) arcos (–0.72) = 136°
4) Since 194° = 360° – 166°,
and 166° < 180°, arcos (–0.97)
= 166°.
12.8.
1) 4
2) 56
3) 0
4) 2
5)
6) does not exist.
12.9.
x = ± 0.45 + 2n.
12.10.
The domain is the segment [–1, 1]. The range
is the segment [0, ].
12.11.
1) No, because we lost negative values of the
argument.
2) No, because on this interval, the cosine is
not monotonic.
3) Yes. On this interval, the cosine is monotonic
and takes all values from –1 to 1.
12.12.
Take the graph of arcos x (see Fig. 3)
and shift it five units to the left.
12.13.
