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A mapping f: R → R which is defined a s f( x ) = cos x; x ε R is
- a)one-one only
- b)onto only
- c)one-one onto
- d)neither one-one nor onto
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A mapping f: R → R which is defined a s f( x ) = cos x; x &epsilo...
Given , f(x) = cos x
It is clear from the figure that f(x) is neither one-one nor a onto function.
Since, whenever we drawn a line parallel to x-axis, then it intersects at infinite points to the curve. So, f(x) is not one-one.
And, range o f f ( x ) = [-1, 1]
Codomain of f(x) = R
Range of f(x) ≠ codomain of f(x)
Hence, f(x) is not onto.
It is clear from the figure that f(x) is neither one-one nor a onto function.
Since, whenever we drawn a line parallel to x-axis, then it intersects at infinite points to the curve. So, f(x) is not one-one.
And, range o f f ( x ) = [-1, 1]
Codomain of f(x) = RRange of f(x) ≠ codomain of f(x)
Hence, f(x) is not onto.
Most Upvoted Answer
A mapping f: R → R which is defined a s f( x ) = cos x; x &epsilo...
Given , f(x) = cos x
It is clear from the figure that f(x) is neither one-one nor a onto function.
Since, whenever we drawn a line parallel to x-axis, then it intersects at infinite points to the curve. So, f(x) is not one-one.
And, range o f f ( x ) = [-1, 1]
Codomain of f(x) = R
Range of f(x) ≠ codomain of f(x)
Hence, f(x) is not onto.
It is clear from the figure that f(x) is neither one-one nor a onto function.
Since, whenever we drawn a line parallel to x-axis, then it intersects at infinite points to the curve. So, f(x) is not one-one.
And, range o f f ( x ) = [-1, 1]
Codomain of f(x) = RRange of f(x) ≠ codomain of f(x)
Hence, f(x) is not onto.
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A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer?
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A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer?.
A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A mapping f: R → R which is defined a s f( x ) = cos x; x ε R isa)one-one onlyb)onto onlyc)one-one ontod)neither one-one nor ontoCorrect answer is option 'D'. Can you explain this answer?.
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