Let `fa n dg` be increasing and decreasing functions, respectively, from `[0,oo]to[0,oo]dot` Let `h(x)=f(g(x))dot` If `h(0)=0,` then `h(x)-h(1)` is always zero (b) always negative always positive (d) strictly increasing none of these

Let f(x)=x+f(x-1)forAAx in RdotIff(0)=1,fin df(100)dot

Let f(x) be a non-constant twice differentiable function defined on (oo, oo) such that f(x) = f(1-x) and f"(1/4) = 0 . Then

Let f(x)=e^(e^(|x|sgnx))a n dg(x)=e^(e^(|x|sgnx)),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=log(f(x))+log(g(x))dot Then for real x , h(x) is (a)an odd function (b)an even function (c)neither an odd nor an even function (d)both odd and even function

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

Let f be a twice differentiable function such that f^(primeprime)=-f(x),a n df^(prime)(x)=g(x),h(x)=[f(x)]^2+[g(x)]^2dot Find h(10)ifh(5)=11

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.

Which of the following statement is always true? (a)If f(x) is increasing, then f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

If fa n dg are two distinct linear functions defined on R such that they map [-1,1] onto [0,2] and h : R-{-1,0,1}vecR defined by h(x)=(f(x))/(g(x)), then show that |h(h(x))+h(h(1/x))|> 2.

If fogoh(x) is an increasing function, then which of the following is possible? (a) f(x),g(x),a n dh(x) are increasing (b) f(x)a n d h(x) are increasing and g(x) is decreasing (c) f(x),g(x),a n dh(x) are decreasing

If f(x) is differentiable and strictly increasing function, then the value of ("lim")_(xvec0)(f(x^2)-f(x))/(f(x)-f(0)) is 1 (b) 0 (c) -1 (d) 2