The maximum domain the a function is provided by all the worths in which the is fine defined:
#"Domain" = x in RR and also f(x) " is defined"#
Since the sine role is characterized everywhere top top the real numbers, its set is #RR#.
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As #f# is a regular function, its variety is a bounded interval given by the max and min worths of the function. The maximum output of #sinx# is #1#, while its minimum is #-1#.
Hence:
#"Range" =
The selection depends on the authorize of #A#. However, if we allow that
#
then the range is much more simply identified as
As a conclusion,
#f:RR ->
Answer attach
Sridhar V.
Jul 26, 2018
#" "#Domain:
#color(blue)((-oo
Interval Notation: #color(green)((-oo, oo)#
Range:
#color(blue)((-1
Interval Notation: #color(green)(<-1, 1>#
Explanation:
#" "#Domain and range of a SIN Graph:
Let united state look in ~ the SIN Graph first:
#color(blue)("Domain :"#
The domain of a duty is the set of entry values for which the duty is real and also defined.
#color(blue)((-oo
Domain restriction provided for the SIN Graph to display screen ONE complete cycle.
#color(blue)("Range :"#
The collection of output worths (of the dependency variable) for which the role is defined.
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As you can conveniently observe, the SIN graph go up until #color(blue)(1# and also goes down until #color(blue)(-1#
#color(blue)((-1
Hope this helps.
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