Statement-1: `e^x + e^-x gt 2 + x^2, x!=0` Statement-2: `f(x) = e^x + e^-x- 2 - x^2` is an increasing function.

statement: e^(pi) is bigger than pi^(e) statement 2:f(x)=x^((1)/(x)) is an increasing function whenn xe[e,oo)

statement1: e^pi is bigger than pi^e statement 2: f(x)=x^(1/x) is an increasing function whenn xe[e,oo)

Show that the function f(x) = (x - 1) e^(x)+2 is strictly increasing function forall x gt 0 .

Consider the following statements 1 f(x)=In x is an increasing funciton on (0,oo) 2 f(x) =e^(x)-x(In x) is an increasing function on (1,oo) Which of the above statement is / are correct ?

If f(x) = (e^x -e^-x)/(e^x +e^-x) + 2 , then the inverse function will be

f(x) = ((e^(2x)-1)/(e^(2x)+1)) is

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)