CSIR-NET June 2019 Question 25 : Real Analysis (Continuous & one-one Function)

[@deepachauhan3657]

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[@RITESHKUMAR-fq6js]

Very conceptual probblem

[@neetu896]

Thank you so much. It helped me a lot.

[@titukumar7756]

thank you sir

[@P.DEY1729]

Sir for the 4th option we can also take the function f(x)=1/(eˣ +1) ?

[@liyaaak912]

Please solve nbhm questions also

[@Axiomatikos]

Ya we will do that too

[@wasimkabir9737]

Thanks you so much sir

[@venkatesuvelpula3775]

How tanhx continuous and 1-1explain?

[@Axiomatikos]

tanh(x) = exp(x)-exp(-x) / exp(x)+exp(-x) Which is quotient of two continuous functions and denominator is never zero. So it is continuous. To prove that it is one-one. Take tanh(x)=tan(y) . Then after little calcution you will get x=y. Which implies tanh(x) is one-one. Also. You can see the graph of tanh(x).