Commerce (English Medium) कक्षा १२ - CBSE Question Bank Solutions

Let A and B be two sets, each with a finite number of elements. Assume that there is an injective map from A to B and that there is an injective map from B to A. Prove that there is a bijection from A to B.

If f : A → A, g : A → A are two bijections, then prove that fog is an injection ?

If f : A → A, g : A → A are two bijections, then prove that fog is a surjection ?

Which one of the following graphs represents a function?

Which of the following graphs represents a one-one function?

If A = {1, 2, 3} and B = {a, b}, write the total number of functions from A to B.

If A = {a, b, c} and B = {−2, −1, 0, 1, 2}, write the total number of one-one functions from A to B.

Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.

If f : R → R is defined by f(x) = x², write f⁻¹ (25)

If f : C → C is defined by f(x) = x², write f⁻¹ (−4). Here, C denotes the set of all complex numbers.

If f : R → R is given by f(x) = x³, write f⁻¹ (1).

Let C denote the set of all complex numbers. A function f : C → C is defined by f(x) = x³. Write f⁻¹(1).

Let f  be a function from C (set of all complex numbers) to itself given by f(x) = x³. Write f⁻¹ (−1).

If f : C → C is defined by f(x) = x⁴, write f⁻¹ (1).

If f : R → R is defined by f(x) = x², find f⁻¹ (−25).

If f : C → C is defined by f(x) = (x − 2)³, write f⁻¹ (−1).

If f : R → R is defined by f(x) = 10 x − 7, then write f⁻¹ (x).

Let \[f : \left( - \frac{\pi}{2}, \frac{\pi}{2} \right) \to R\]  be a function defined by f(x) = cos [x]. Write range (f).

If f : R → R defined by f(x) = 3x − 4 is invertible, then write f⁻¹ (x).