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A function f: R → R defined as f(x) = x4 is
- a)neither one-one nor onto
- b)many-one and onto
- c)one-one but not onto
- d)one-one and onto
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A function f: R → R defined as f(x) = x4isa)neither one-o...
f: R → R is defined as f(x) = x4
Let x, y ∈ R such that f(x) = f(y).
=> x4 = y4
=> x =+-y
Therefore, f(x1) = f(x2) does not imply that x1=x2.
For instance,f(1) = f(-1) = 1
∴ f is not one-one.
Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2.
∴ f is not onto.
Hence, function f is neither one-one nor onto.
Let x, y ∈ R such that f(x) = f(y).
=> x4 = y4
=> x =+-y
Therefore, f(x1) = f(x2) does not imply that x1=x2.
For instance,f(1) = f(-1) = 1
∴ f is not one-one.
Consider an element 2 in co-domain R. It is clear that there does not exist any x in domain R such that f(x) = 2.
∴ f is not onto.
Hence, function f is neither one-one nor onto.
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A function f: R → R defined as f(x) = x4isa)neither one-o...
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A function f: R → R defined as f(x) = x4isa)neither one-one nor ontob)many-one and ontoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A function f: R → R defined as f(x) = x4isa)neither one-one nor ontob)many-one and ontoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A function f: R → R defined as f(x) = x4isa)neither one-one nor ontob)many-one and ontoc)one-one but not ontod)one-one and ontoCorrect answer is option 'A'. Can you explain this answer?.
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