Related InterviewSolutions

• If A = {a,b,c}, B = {u, v, w}. if f: A → B and g : B → A, defined as f = {(a, v), (b, u), (c, w)}, g = {(u, b), (v, a), (w, c)} then find (fog) and (gof).
• If f : R → R, f(x) = 2x + 1 and g : R → R, g(x) = x3, then (gof)-1(27) is equal to :(a) 2(b) 1(c) -1(d) 0
• If f: R → R and g: R+ R, where f(x) = 2x + 3 and g(x) = x2 + 1, then (gof)(2):(a) 38(b) 42(c) 46(d) 50
• If functions f and g be defined as below, then find (gof)(x) : f : R → R, f(x) = 2x + x-2 g : R → R, g(x) = x4 + 2x + 4
• If f, g, h be three functions from R to R, defined as f(x) = x2, g(x) = cos x and h(x) = 2x + 3, then find {ho(gof)} (√2π).
• Which of the following operations is commutative in R:(a) a*b = a2b(b) a*b = ab(c) a*b = a – b + ab(d) a * b = a + b + a2b
• Subtraction is an operation on Z, which is(a) commutative and associative(b) associative but not commutative(c) neither commutative and nor associative(d) commutative but not associative
• If f: R+ → R+ and g : R+ → R+, defined as f(x) = x2, g(x) = √x, then find gof and fog wheather are they equivalent ?
• If A = {1, 2, 3,4}, B = {a,b,c,d}, then define four bijection from A to B and also find their inverse functions.
• If f : R → R,f(x) = cos (x + 2), is f-1 exists.