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 ?

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

Consider the following statements I.y=(e^(x)+e^(-x))/(2) is an increasing function on [0,oo). II.y=(e^(x)-e^(-x))/(2) is an increasing function on (-oo,oo). Which of the above statement(s) is/are correct?

Consider the following statements: 1. The function f(x)=|x| is not differentiable at x=1. 2. The function f(x)=e^(x) is not differentiable at x=0. Which of the above statements is/are correct ?

Consider the following statements: I. The function f(x)=|x| is not differentiable at x = 1 II. The function f(x)=e^(x) is differentiable at x = 0 Which of the above statements is/are correct?

Consider the following statements : 1. The function f(x)=x^(2)+2cosx is increasing in the interval (0,pi) 2. The function f(x)=1n(sqrt(1+x^(2)-x)) is decreasing in the interval (-oo,oo) Which of the above statements is/ are correct ?

A function f:RtoR is defined as f(x)=x^(2)" for "xge0,f(x)=-x" for "xlt0 . Consider the following statements in respect of the above function : 1. The function is continuous at x=0. 2. The function is differentiable at x=0. Which of the above statements is /are correct ?

Consider the following statements I.The function f(x)=x^(2)+2cos x is increasing in the interval (0,pi). II.The function f(x)=ln(sqrt(1+x^(2))-x) is decreasing in the interval (-oo,oo). Which of the above statement(s) is/are correct?

Prove that the function f(x)=log_(e)x is increasing on (0,oo)