Define a function as a set of ordered pairs. Watch Solution
Define a function as a correspondence between two sets. Watch Solution
What is the fundamental difference between a relation and a function? Is every relation a function ? Watch Solution
let A = {-2,-1,0,1,2} and f:A→Z be a function defined by f (x) = x^2 – 2x – 3. Find : (i) range of f i.e f(A) (ii) pre image of 6, -3 and 5 Watch Solution
if a function f:R →R be defined f(x) = {3x-2 ,x less than 0 ; 1, x=0 ; 4x+1, x > 0 Watch Solution
A function f:R→R is defined by f(x) = x^2. Determine (i) range of f (ii) {x : f(x) = 4} (iii) {y : f(y) = -1}. Watch Solution
Let f:R^+→R, where R^+ is the set of all positive real numbers, be such that f(x)=loge x. Determine (i) the image set of the domain of f (ii) {x : f(x) = -2} (iii) whether f(xy) = f(x) + f(y) holds. Watch Solution
Write the following relation as sets of ordered pairs and is it function ?{(x, y) : y = 3x, x∈{1, 2, 3}, y∈{3, 6, 9, 12}}. Watch Solution
Write the following relation as sets of ordered pairs and is it function ? {(x, y) : y greater than x + 1, x = 1, 2 and y = 2, 4, 6} Watch Solution
Write the following relation as sets of ordered pairs and is it function ? {(x, y) : x + y = 3 x, y∈{0, 1, 2, 3}} Watch Solution
let f:R→R and g:C→C be two functions defined as f (x) = x^2 and g(x) = x^2. are they equal functions ? Watch Solution
If f, g, h are three functions defined from R to R as follows: (I) f(x) = x^2 (ii) g(x) = sin x (iii) h (x) = x^2 + 1 Find the range of each function. Watch Solution
find the range of each function. let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16} Determine which of the following sets are functions from X to Y (i) f1 = {(1, 1), (2, 11), (3, 1), (4, 15)} (ii) f2 = {(1, 1), (2, 7), (3, 5)} (iii) f3 = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Watch Solution
let A = {12,13,14,15,16,17} and f:A→Z be a function given by f(x) = highest prime factor of x. Find range of f. Watch Solution
If f:R→R be defined by f(x) = x^2 + 1, then find f^-1{17} and f^-1{-3}. Watch Solution
Let A = {p, q ,r, s} and B = {1, 2, 3}. Which of the following relations from A to B is not a function ? (i) R1 = {(p, 1), (q, 2), (r, 1), (s, 2)} (ii) R2 = {(p, 1), (q, 1), (r, 1), (s, 1)} (iii) R3 = {(p, 1), (q, 2), (p, 2), (s, 3)} (iv) R4 = {(p, 2), (q, 3), (r, 2), (s, 2)}. Watch Solution
Let A = {9,10,11,12,13} and let f:A→N be defined by f(n) = the highest prime factor of n. Find the range of f. Watch Solution
The function f is defined by f(x) = {x^2, 0≤x≤3 ; 3x, 3≤x≤10 The relation g is defined by g(x) = {x^2, 0≤x≤2 ; 3x, 2≤x≤10 Show that f is a function and g is not a function.Watch Solution
If f (x) = x^2, find {f(1.1) – f(1)}/{(1.1) – 1} Watch Solution
Express the function f:X→R given by f(x) = x^3 + 1 as set of ordered pairs, where X = {-1, 0, 3, 9, 7}. Watch Solution
Chapter 3: Functions – R. D. Sharma Class 11th Maths