Let `f(x)` be an increasing function defined on `(0,oo)` . If `f(2a^2+a+1)>f(3a^2-4a+1),` then the possible integers in the range of `a` is/are `1` (b) 2 (c) 3 (d) 4

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

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

A function is defined by f(x)=2x-3 Find (f(0)+f(1))/(2) .

If f(x+1/2)+f(x-1/2)=f(x) for all x in R , then the period of f(x) is 1 (b) 2 (c) 3 (d) 4

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5

Let f be a continuous function defined onto [0,1] with range [0,1]. Show that there is some c in [0,1] such that f(c)=1-c

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)

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

Let A, B, C in N and a function f:A to B be defined by f(x)=2x+1 and g: B to C be defined by g(x)=x^(2) . Find the range of fog and gof.

Let A, B, C in N and a function f:A to B be defined by f(x)=2x+1 and g: B to C be defined by g(x)=x^(2) . Find the range of fog and gof.