Let f is a real valued function defined on the interval `(-1,1)` such that `e^(-x)f(x) = 2 + int_0^x sqrt(t^4 + 1 dt) AA x in (-1,1) and f^(-1)` is the inverse of f. If `(f^(-1)(2)) = 1/k` then k is

Let f be a real -valued function defined on the interval (-1, 1) such that e^(-x)f(x) = 2+int_(0)^(x) sqrt(t^(4) + 1)dt for all x in (-1, 1) and let f^(-1) be the inverse function of f. then show that (f^(-1)(2))^1 = (1)/(3)

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

If f(x) is a real function defined on [-1,1], then the function g(x) = f(5x+4) is defined on the interval

If f(x) is a real function defined on [-1, 1], then the real function g(x) = f(5x + 4) is defined on the interval

If f(x) = int_(0)^(x) t.e^(t) dt then f'(-1)=

If f(x) = int_1^x (1)/(2 + t^4) dt ,then

Let 'f' be a real valued function defined for all x in R such that for some fixed a gt 0, f(x+a)= 1/2 + sqrt(f(x)-(f(x))^(2)) for all 'x' then the period of f(x) is

Let f:[4, infty) to [1, infty) be a function defined by f(x) = 5^(x(x-4)) , then f^(-1)(x) is