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

• 4

• -4

• 0

• 0

Let f : R → R be a positive increasing function with 

• 1

• 2/3

• 3/2

• 3/2

If for  x ∈ (0, 1/4)  the derivatives  then g(x) is equals to 

• π/2

• 1

• -1

• -1

For 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.

428.

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