Domain of f(x)= the set of all real x for which f(x) is a real number. Find out whether the domains of the following two functions coincide (if they do not then find the common part of the domains of the functions being compared ) y=cosπx and y=cotπx
Answers
Given : Domain of f(x)= the set of all real x for which f(x) is a real number.
y=cosπx and y=cotπx
To find : whether the domains of the following two functions coincide (if they do not then find the common part of the domains of the functions being compared )
Solution:
y=cosπx
cosπx is defined for all values
Domain of cosπx is R
y=cotπx
= cosπx / Sinπx
y=cotπx not defined if Sinπx = 0
Sinπx = 0
=> πx = nπ where n ∈ Z
Hence Domain of cotπx is R - Z
Domain of cosπx is R
Domain of cotπx is R - Z
Hence domains of two functions does not coincide
the common part of the domains of the functions being compared
R ∩ (R - Z)
= R - Z
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