PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Classify the following function as injection, surjection or bijection :

f : Q → Q, defined by f(x) = x³ + 1

Classify the following function as injection, surjection or bijection :
f : R → R, defined by f(x) = 5x³ + 4

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 3 − 4x

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = 1 + x²

Classify the following function as injection, surjection or bijection :

f : R → R, defined by f(x) = `x/(x^2 +1)`

If f : A → B is an injection, such that range of f = {a}, determine the number of elements in A.

Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.

Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : `f (x) = x/2`

Let A = [-1, 1]. Then, discuss whether the following function from A to itself is one-one, onto or bijective : g(x) = |x|  

Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x² 

Set of ordered pair of  a function? If so, examine whether the mapping is injective or surjective :{(x, y) : x is a person, y is the mother of x}

Set of ordered pair of a function ? If so, examine whether the mapping is injective or surjective :{(a, b) : a is a person, b is an ancestor of a} 

Let A = {1, 2, 3}. Write all one-one from A to itself.

If f : R → R be the function defined by f(x) = 4x³ + 7, show that f is a bijection.

Show that the exponential function f : R → R, given by f(x) = e^x, is one-one but not onto. What happens if the co-domain is replaced by`R0^+` (set of all positive real numbers)?

Show that the logarithmic function  f : R0⁺ → R   given  by f (x)  log_a x ,a> 0   is   a  bijection.

If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.

If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.

Find the number of all onto functions from the set A = {1, 2, 3, ..., n} to itself.

Give examples of two one-one functions f₁ and f₂ from R to R, such that f₁ + f₂ : R → R. defined by (f₁ + f₂) (x) = f₁ (x) + f₂ (x) is not one-one.