Statement 1: The function `f(x)=x` In `x` is increasing in `(1/e ,oo)` Statement 2: If both `f(x)a n dg(x)` are increasing in `(a , b),t h e nf(x)g(x)` must be increasing in (a,b).

Show that the function given by f (x) = e ^(2x) is increasing on R.

Statement 1: f(x)=x+cosx is increasing AAx in Rdot Statement 2: If f(x) is increasing, then f^(prime)(x) may vanish at some finite number of points.

Prove that f(x)=x-sinx is an increasing function.

Statement 1: The function f(x)=x^4-8x^3+22 x^2-24 x+21 is decreasing for every x in (-oo,1)uu(2,3) Statement 2: f(x) is increasing for x in (1,2)uu(3,oo) and has no point of inflection.

Statement 1: Both f(x)=2cos x+3sinxa n dg(x)=sin^(-1)x/(sqrt(13))-tan^(-1)3/2 are increasing in (0, pi /2) Statement 2: If f(x) is increasing, then its inverse is also increasing.

The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decreasing in (0,oo) increasing in (0,pi/e), decreasing in (pi/e ,oo) decreasing in (0,pi/e), increasing in (pi/e ,oo)

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)' must be

Consider the function f:(-oo,oo)vec(-oo,oo) defined by f(x)=(x^2+a)/(x^2+a),a >0, which of the following is not true? maximum value of f is not attained even though f is bounded. f(x) is increasing on (0,oo) and has minimum at ,=0 f(x) is decreasing on (-oo,0) and has minimum at x=0. f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1,t h e n[f(x)]^(g(x)) is increasing.