Give an example of a function (i) Which is one – one but not onto. Watch Solution
Give an example of a function (ii) Which is not one – one but onto. Watch Solution
Give an example of a function (iii) Which is neither one-one nor onto. Watch Solution
Is function from A to B one–one and onto ? f1 = {(1, 3), (2, 5), (3, 7)}; A = {1, 2, 3}, B = {3, 5, 7} Watch Solution
Is function from A to B one–one and onto ? f2 = {(2, a), (3, b), (4, c)}; A = {2, 3, 4}, B = {a, b, c} Watch Solution
Is function from A to B one–one and onto ? f3 = {(a, x), (b, x), (c, z), (d, z)}; A = {a, b, c, d}, B = {x, y, z} Watch Solution
Prove that the function f : N → N, defined by f(x) = x^2 + x + 1 is one–one but not onto. Watch Solution
Let A = {-1, 0, 1} and f = {(x, x^2) : x ∈ A}. Show that f : A → A is neither one–one nor onto. Watch Solution
Check the function as injection, surjection or bijection: f : N → N given by f(x) = x^2 Watch Solution
Check the function as injection, surjection or bijection : f : Z → Z given by f(x) = x^2 Watch Solution
Check the function as injection, surjection or bijection : f : N → N given by f(x) = x^3 Watch Solution
Check the function as injection, surjection or bijection : f : Z → Z given by f(x) = x^3 Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = |x| Watch Solution
Check the function as injection, surjection or bijection : f : Z → Z, defined by f(x) = x^2 + x Watch Solution
Check the function as injection, surjection or bijection : f : Z → Z, defined by f(x) = x – 5 Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = sin x Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = x^3 + 1 Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = x^3 – x Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = sin^2 x+cos^2 x Watch Solution
Check the function as injection, surjection or bijection : f: Q – {3} → Q, defined by f(x)=(2x+3)/(x-3) Watch Solution
Check the function as injection, surjection or bijection : f : Q → Q, defined by f(x) = x^3 + 1 Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x)=5x^3 + 4 Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x) = 3 – 4x Watch Solution
Check the function as injection, surjection or bijection : f : R → R, defined by f(x)=1+ x^2 Watch Solution
Check the function as injection, surjection or bijection : f: R → R, defined by f(x)=x/(x^2 +1) Watch Solution
If f: A → B is an injection such that range of f = {a}. Determine the number of elements in A. Watch Solution
Show that the function f : R – {3} → R – {1} given by f(x) = (x – 2)/(x – 3) is a bijection. Watch Solution
Let A = [-1, 1], Then, discuss whether the following function from A to itself are one–one, onto, or bijective: f(x)=x/2 Watch Solution
Let A = [-1, 1], Then, discuss whether the following function from A to itself are one–one, onto, or bijective: g(x)=∣x∣ Watch Solution
Let A = [-1, 1], Then, discuss whether the following function from A to itself are one–one, onto, or bijective : h(x)=x^2 Watch Solution
Are the following set of ordered pairs function ? If so, examine whether the mapping is injective or surjective: {(x, y): x is a person, y is the mother of x} Watch Solution
Are the following set of ordered pairs function ? If so, examine whether the mapping is injective or surjective: {(a, b) : a is a person, b is an ancestor of a} Watch Solution
Let A = {1, 2, 3}. Write all one – one from A to itself. Watch Solution
If f : R → R be the function defined by f(x) = 4x^3 + 7, show that f is a bijection. Watch Solution
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). Watch Solution
Show that the logarithmic function f : R0+→ R given by f(x) = loga x, a greater than 0 is a bijection.Watch Solution
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto. Watch Solution
If A = {1, 2, 3}, show that an onto function f : A → A must be one – one. Watch Solution
Find the number of all onto functions from the set A = {1, 2, 3, …., n} to itself. Watch Solution
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. Watch Solution
Give examples of two surjective functions f1 and f2 from Z to Z such that f1 + f2 is not surjective. Watch Solution
Show that if f1 and f2 are one – one map from R to R, then the product f1 × f2 : R → R defined by (f1 × f2)(x) = f1(x)f2(x) need not be one – one. Watch Solution
Suppose f1 and f2 are non–zero one–one functions from R to R. Is f1/f2 necessarily one – one? Justify your answer. Here, f1/f2 :R→R is given by (f1/f2)(x)=f1(x)/f2(x) for all x ∈ R. Watch Solution
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following: (i)an injective map from A to B (ii)a mapping from A to B which is not injective (iii) a mapping from A to B Watch Solution
Show that f : R → R, given by f(x) = x – [x], is neither one – one nor onto. Watch Solution
Let f : N → N be defined by f(n)={n+1, if n is odd ; n−1,if n is even Show that f is a bijection. Watch Solution
