Let `f(x) = x^4 + x` defined on `[0, 3].` Extend the function `f(x)` so that f is even. If value of the extended function at `-3` is `K,` then `1/42 K` is equal to.

Extend f(x)=x^2+x defined in [0,3] onto the interval[-3,3] so that f(x) is even

In the function f(x) is defined for x in[0,1] then the function f(2x+3) is defined for

The function f(x)=(x^2-1)/(x^3-1) is not defined for x=1. The value of f(1) so that the function extended by this value is continuous is

Let f : R rarr R be the functions defined by f(X) = x^3 + 5 , then f^-1 (x) is

Let f(x)=x(2-x), 0 le x le 2 . If the definition of 'f' is extended over the set R-[0, 2] by f(x+1)=f(x) then f is a periodic function with period.

Let f be a real valued function defined on (0, 1) cup (2, 4) , such that f(x)=0 , for every x, then :

Let f : [-3, 3] rarr R defined by f(x) = [(x^(2))/(a)] tan ax + sex ax . Then If f(x) is an even function, then

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 to R is a function defined as f(x) where = {(|x-[x]| ,:[x] "is odd"),(|x - [x + 1]| ,:[x] "is even"):} [.] denotes the greatest integer function, then int_(-2)^(4) dx is equal to