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Maths-

General

Easy

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 $g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals$ $g to the power of negative 1 end exponent$
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.

only III
both I & III
both I & II
I, II, III

hint Hint:

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 $g o f equals I subscript A text and end text fog equals I subscript B comma text then end text f equals$ $g to the power of negative 1 end exponent$ .

The correct answer is: both I & II

Both I and II are correct statement.

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