Multiple Choice QuestionsFor real x, let f(x) = x3+ 5x + 1, then
f is one–one but not onto R
f is onto R but not one–one
f is one–one and onto R
f is one–one and onto R
Let f(x) = (x + 1)2– 1, x ≥ – 1
Statement – 1: The set {x : f(x) = f–1(x)} = {0, –1}.
Statement – 2: f is a bijection.
Statement–1 is true, Statement–2 is true,Statement–2 is a correct explanation for statement–1
Statement–1 is true, Statement–2 is true; Statement–2 is not a correct explanation for statement–1.
Statement–1 is true, statement–2 is false.
Statement–1 is true, statement–2 is false.
Let f(x) = x|x| and g(x) = sinx
Statement 1 : gof is differentiable at x = 0 and its derivative is continuous atthat point
Statement 2: gof is twice differentiable at x = 0
Statement–1 is true, Statement–2 is true, Statement–2 is a correct explanation for statement–1
Statement–1 is true, Statement–2 is true;Statement–2 is not a correct explanation for statement–1.
Statement–1 is true, statement–2 is false.
Statement–1 is true, statement–2 is false.
Let f : N → Y be a function defined as f (x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3 for some x ∈ N}.Show that f is invertible and its inverse is
Let R be the real line. Consider the following subsets of the plane R × R.
S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x − y is an integer}. Which one of the following is true?
neither S nor T is an equivalence relation on R
both S and T are equivalence relations on R
S is an equivalence relation on R but T is not
S is an equivalence relation on R but T is not
Let f(x) = 
Then which one of the following is true?
f is neither differentiable at x = 0 nor at x = 1
f is differentiable at x = 0 and at x = 1
f is differentiable at x = 0 but not at x = 1
f is differentiable at x = 0 but not at x = 1
Switch
then g(x) is equals to 
[cot x]dx, where [.] denotes the greatest integer function, is equal to
