Let f be a function defined for every x, such that `f''=-f`, f(0)=0,f'(0) =1 then f(x) is equal to

Let f be function defined for every x , such that f^(11) = -f ,f(0) = 0 , f^(1)(0)=1 then f(x) is equal to

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f be a function defined on [a, b] such that f'(x)>0 for all x in (a,b) . Then prove that f is an increasing function on (a, b) .

Let f(x) be a function such that,f(0)=f'(0)=0,f''(x)=sec^(4)x+4 then the function is

Let f :R->R be a function defined by f(x)=|x] for all x in R and let A = [0, 1), then f^-1 (A) equals

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then