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Let f : A→B and g : B→C be one-one functions. Then, gof: A→C is
- a)one-one
- b)does not exist
- c)not onto
- d)onto
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Let f : A→B and g : B→C be one-one functions. Then, gof: A...
We are given that functions f : A→B and g : B→C are both one-to-one functions.
Suppose a1, a2 ∈ A such that (gof)(a1) = (gof)(a2)
⇒ g(f(a1)) = g(f(a2)) (definition of composition) Since g is one-to-one, therefore,
f(a1) = f(a2)
And since f is one-to-one, therefore, a1 = a2
Thus, we have shown that if (gof)(a1) = (gof)(a2) then a1 = a2
Hence, gof is one-to-one function.
Suppose a1, a2 ∈ A such that (gof)(a1) = (gof)(a2)
⇒ g(f(a1)) = g(f(a2)) (definition of composition) Since g is one-to-one, therefore,
f(a1) = f(a2)
And since f is one-to-one, therefore, a1 = a2
Thus, we have shown that if (gof)(a1) = (gof)(a2) then a1 = a2
Hence, gof is one-to-one function.
Most Upvoted Answer
Let f : A→B and g : B→C be one-one functions. Then, gof: A...
f is one-one g is one-oneIf f(x1) = f(x2)
If g(x2) = g(x2)then x1 = x2 then x1= x2C
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Community Answer
Let f : A→B and g : B→C be one-one functions. Then, gof: A...
If f : A gives B g: B gives C nd its one one function then gof ( means g is a function of f ) then A gives C will also be one one
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Let f : A→B and g : B→C be one-one functions. Then, gof: A→C isa)one-oneb)does not existc)not ontod)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 Let f : A→B and g : B→C be one-one functions. Then, gof: A→C isa)one-oneb)does not existc)not ontod)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 Let f : A→B and g : B→C be one-one functions. Then, gof: A→C isa)one-oneb)does not existc)not ontod)ontoCorrect answer is option 'A'. Can you explain this answer?.
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