Sir I saw many you tube channels ,all of them thaught the same but the way you help us learn things ,it's very unique...sir please upload video continuously ,we want them
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).
Sir I saw many you tube channels ,all of them thaught the same but the way you help us learn things ,it's very unique...sir please upload video continuously ,we want them
thank you sir
Thank you so much. It helped me a lot.
Sir for the 4th option we can also take the function f(x)=1/(eˣ +1) ?
Very conceptual probblem
Please solve nbhm questions also
Ya we will do that too
How tanhx continuous and 1-1explain?
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).
Thanks you so much sir