Let f={(1,1),(2,3),(0,-1),(,-1,-3)} be a linear function from Z into Z. Find f(x).

Let f={(1,1),(2,3),(0,-1),(-1,-3)} be a function from Z to Z defined by f(x)= ax + b, for some integers a, b. Determine a, b,

Let E={1, 2, 3, 4} and F= {1, 2} . Then the number of onto functions from E to F is

Let f : (-1, 1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x) + 2)]^2 . Then g'(0) is equal to

Let A (1,2,-1) , B(2,1,3) and if the length of projection of segment vec (AB) on the plane x - 2y - 2z =1 is d then the value of [d] (where [] is G.I.F)

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

If [{:(x-1," "2,5-y),(" "0,z-1,7),(" "1," "0,a-5):}]=[{:(1,2,3),(0,4,7),(1,0,0):}] then find the values of x , y z and a .