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Question

Statement I :f colon A not stretchy rightwards arrow B text  is one - one and  end text g colon B not stretchy rightwards arrow C text  is a one-one function, then gof  end text colon A not stretchy rightwards arrow C is one - one
Statement II :text  If  end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A are two functions such that g o f equals I subscript A text  and  end text fog equals I subscript B comma text  then  end text f equalsg to the power of negative 1 end exponent
Staatement III : f left parenthesis x right parenthesis equals sec squared invisible function application x minus tan squared invisible function application x g left parenthesis x right parenthesis equals cosec squared invisible function application x minus cot squared invisible function application x comma text  then  end text f equals g

Which of the above statement/s is/are true.

  1. only III
  2. both I & III
  3. both I & II
  4. I, II, III

hintHint:

As we know that if f colon A not stretchy rightwards arrow B text  is one - one and  end text g colon B not stretchy rightwards arrow C text  is a one-one function, then gof  end text colon A not stretchy rightwards arrow C is one-one and text  If  end text f colon A not stretchy rightwards arrow B comma g colon B not stretchy rightwards arrow A are two functions such that g o f equals I subscript A text  and  end text fog equals I subscript B comma text  then  end text f equalsg to the power of negative 1 end exponent.

The correct answer is: both I & II


    Both I and II are correct statement.

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