Let A = {xϵR :–1≤x≤1} =B and C={xϵR :X ≥ 0} and let S={(x, y) ϵA×B :x^2+y^2=1} and S0={(x, y)ϵA×C :x^2+y^2=1} Then A. S defines a function from A to B B. S0 defines a function from A to C C. S0 defines a function from A to B D. S defines a function from A to C Watch Solution
f:R→R given by f(x) = x + √x^2 is A. injective B. surjective C. bijective D. none of these Watch Solution
If f : A → B given by 3^f(x)+2^−x= 4 is a bijection, then Watch Solution
The function f : R → R defined by f(x) = 2^x + 2^∣x∣ is A. one-one and onto B. many-one and onto C. one-one and into D. many-one and into Watch Solution
Let the function f:R- {-b}→R- {1} be defined by f(x)= (x+a)/(x+b), a ≠ b, then A. f is one-one but not onto B. f is onto but not one-one C. f is both one-one and onto D. none of these Watch Solution
The function f : A → B defined by f(x)=−x^2+6x-8 is a bijection, if A. A = (- ∞, 5] and B = (-∞, 1] B. A = [- 3, ∞] and B = (-∞, 1] C. A = (–∞, 3] and B = [1, ∞) D. A = [3, ∞) and B = [1, ∞) Watch Solution
Let A = {x ϵR : –1 ≤ x ≤ 1} = B. Then, the mapping f : A → B given by f(x) = x |x| is A. injective but not surjective B. surjective but not injective C. bijective D. none of these Watch Solution
Let f:R→R be given by f(x)=[x]^2+[x+1]−3, where [x] denotes the greatest integer less than or equal to x. Then, f(x) is (a) many-one and onto (c) one-one and into (b) many-one and into (d) one-one and onto Watch Solution
Let M be the set of all 2 × 2 matrices with entries from the set R of real numbers. Then the function f : M → R defined by f(A) = |A| for every A ϵ M, is A. one-one and onto B. neither one-one nor onto C. one-one not one-one D. onto but not one-one Watch Solution
The function f: [0,∞)→R given by f(x)=x/(x+1) is A. one-one and onto B. one-one but not onto C. onto but not one-one D. neither one-one nor onto Watch Solution
The range of the function f(x) = 7−x)P(x−3 is A. {1, 2, 3, 4, 5} B. {1, 2, 3, 4, 5, 6} C. {1, 2, 3, 4} D. {1, 2, 3} Watch Solution
A function f from the set on natural numbers to integers defined by .f(n)={n−1 /2,when n is odd : −n/2, when n is even is A. neither one-one nor onto B. one-one but not onto C. onto but not one-one D. one-one and onto both Watch Solution
Let f be an injective map with domain {x, y, z} and range {1, 2, 3} such that exactly one of the following statements is correct and the remaining are false.f(x) = 1, f(y) ≠ 1, f(z) ≠ 2.The value of f^−1(1) is A. x B. y C. z D. none of these Watch Solution
Which of the following functions from Z to itself are bijections? A. f(x)=x^3 B. f(x)=x + 2 C. f(x) = 2x + 1 D. f(x) = x^2 + x Watch Solution
Which of the following functions from A={x:−1≤x≤1} to itself are bijections? A. f(x)=x/2 B. g(x)=sin(πx/2) C. h(x)=∣x∣ D. k(x)=x^2 Watch Solution
Let A = {x : – 1 ≤ x ≤ 1} and f : A → A such that f(x) = x |x|, then f is A. a bijection B. injective but not surjective C. surjective but not injective D. neither injective nor surjective Watch Solution
If the function f:R→A given by f(x) = x^2/(x^2+1) is a surjection, then A = A. R B. [0,1] C. (0,1] D. [0,1) Watch Solution
If a function f : [2, ∞) → B defined by f(x) = x^2-4x+5 is a bijection, then B = A. R B. [1, ∞) C. [4, ∞) D. [5, ∞) Watch Solution
The function f : R → R defined by f(x) = (x – 1) (x – 2) (x – 3) is A. one-one but not onto B. onto but not one-one C. both one and onto D. neither one-one nor onto Watch Solution
The function f : [-1/2, 1/2] → [π/2, π/2] defined by f(x)=sin^{-1}(3x – 4x^3) is A. bijection B. injection but not a surjection C. surjection but not an injection D. neither an injection nor a surjection Watch Solution
Let f:R→R be a function defined by f(x)=e^∣x∣-e^-x/ e^x+e^-x. Then, A. f is a bijection B. f is an injection only C. f is surjection on only D. f is neither an injection nor a surjection Watch Solution
Let f : R – {n}→R be a function defined by f(x)= (x-m)/(x-n), where m ≠ n. Then, A. f is one-one onto B. f is one-one into C. f is many one onto D. f is many one into Watch Solution
Let f:R→R be a function defined by f(x)= (x^2-8)/(x^2+2). Then, f is A. one-one but not onto B. one-one and onto C. onto but not one-one D. neither one-one nor onto Watch Solution
f:R→R is defined by f(x)= (e^x^2-e^-x^2)/(e^x^2+e^-x^2) is A. one-one but not onto B. one-one and onto C. onto but not one-one D. neither one-one nor onto Watch Solution
The function f : R → R, f(x)=x^2 is A. injective but not surjective B. surjective but not injective C. injective as well as surjective D. neither injective nor surjective Watch Solution
A function f from the set of natural, numbers to the set of integers defined by f(n)={n−1/2, when n is odd ;−n/2, when n is even A. neither one-one nor onto B. one-one but not onto C. onto but not one-one D. one-one and onto both Watch Solution
Which of the following functions from A={x∈R:−1≤x≤1} to itself are bijections? A. f(x)=∣x∣ B. f(x)=sinπx/2 C. f(x)=sinπx/4 D. none of these Watch Solution
Let f:z→z be given by f(x)= {x/2, , if x is even ; 0, if x is odd .Then, f is A. onto but not one-one B. one-one but not onto C. one-one and onto D. neither one-one nor onto Watch Solution
The function f : R → R defined by f(x) = 6^x+6^∣x∣ is A. one-one and onto B. many one and onto C. one-one and into D. many one and into Watch Solution
Let f(x)=x^2 and g(x)=2^x. Then the solution set of the equation fog(x) = gof (x) is A. R B. {0} C. {0, 2} D. none of these Watch Solution
If f:R→R is given by f(x)=3x−5, then f^−1(x) A. is given by 1/(3x−5) B. is given by (x+5)/3 C. does not exist because f is not one-one D. does not exist because f is not onto Watch Solution
If g(f(x))=∣sinx∣ and f(g(x))=(sin√x)^2, then A. f(x)=sin^2x , g(x)=√x B.f(x)=sinx,g(x)=∣x∣ C. f(x)=x^2,g(x)=sin√x D. f and f cannot be determined Watch Solution
The inverse of the function f:R→[x∈R:x less than1] given by f(x)= (e^x−e^−x)/(e^x+e^−x) , is Watch Solution
Let A={x∈R:x≥1}. The inverse of the function f:A→A given by f(x)=2^x(x−1), is Watch Solution
Let A={x∈R:x≤1} and f:A→ A given by f(x)=x(2−x). Then, f^−1(x) is (a) 1+ √1-x (b) 1-√1-x (c) √1-x (d) 1±√1-x Watch Solution
Let f(x) = 1/(1−x) .Then, {fo(fof)}(x) A. x for all x∈R B. x for all x∈R−{1} C. x for all x∈R−{0,1} D. none of these Watch Solution
If the function f:R→R be such that f(x)=x−[x], where [x] denotes the greatest integer less than or equal to x, then f^−1(x) is (a) 1/(x-[x]) (b) [x] – x (c) not defined (d) none of these Watch Solution
If F: [1,∞)→[2,∞) is given by f(x) = x + 1/x, then f^−1(x) equals. Watch Solution
Let g(x)=1+x−[x] and f(x)={−1, x less than0 : 0, x=0 : 1, x greater than 0 , where [x] denotes the greatest integer less than or equal to x. Then for all x ,f(g(x)) is equal to (a) x (b) 1 (c) f(x) (d) g(x) Watch Solution
Let f(x) = αx/(x+1), x ≠ −1. Then, for what value of a is f(f(x)) = x ? (a) √2 (b) -√2 (c) 1 (d) -1 Watch Solution
The distinct linear functions which map [–1, 1] onto [0, 2] are A. f(x) = x + 1, g(x) = – x + 1 B. f(x) = x – 1, g(x) = x + 1 C. f(x) = –x – 1 g(x) = x – 1 D. none of these Watch Solution
Let f : [2, ∞) → X be defined by f(x) = 4x−x^2. Then, f is invertible, if X = (a) [2,∞) (b) (- ∞, 2] (c) (-∞, 4] (d) [4,∞) Watch Solution
If f : R→(−1,1) is defined by f(x)=−x∣x∣/(1+x^2), then f^−1(x) equals Watch Solution
Let [x] denote the greatest integer less than or equal to x . If f(x)=sin^−1x, g(x)=[x^2] and h(x)=2x, 1/2≤x≤1/√2, then Watch Solution
If g(x) = x^2 + x − 2 and 1/2 gof(x) = 2x^2 − 5x + 2, then f(x) is equal to Watch Solution
If f(x) = sin^2 x and the composite function g(f(x)) = ∣sinx∣, then g(x) is equal to (a) √x-1 (b) √x (c) √x+1 (d) – √x Watch Solution
If f : R→R is given by f(x) = x^3 + 3, then f^−1(x) is equal to (a) x^1/3 -3 (b) x^1/3 +3 (c) (x – 3)^1/3 (d) (x + 3)^1/3 Watch Solution
Let f(x) = x^3 be a function with domain {0, 1, 2, 3}. Then domain of f^−1 is (a) {3, 2, 1, 0} (b) {0,-1,-2, -3} (c) {0, 1, 8, 27} (d) {0,-1,-8, -27} Watch Solution
Let f : R→R be given by f(x) = x^2 – 3. Then ,f^-1 is given by (a) √x + 3 (b) √x + 3 (c) x + √3 (d) none of these Watch Solution
Let f : R→R be given by f(x)=tan x .Then, f^-1(1) is (a) π/4 (b) {nπ+π/4 : n∈Z} (c) does not exist (d) none of these Watch Solution
Let f:R→R be defined as f(x)= {2x, if x greater than 3 ; x^2, if 1 less than x≤3 ; 3x, if x≤1Then, find f(-1)+f(2)+f(4) Watch Solution
Let A={1,2,…,n} and B={a,b}. Then the number of subjections from A into B is (a) nP2 (b) 2^n – 2 (c) 2^n – 1 (d) nC2 Watch Solution
If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is A. 720 B. 120 C. 0 D. none of these Watch Solution
If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is (a) 10C7 (b) 10C7 x7! (c) 7^10 (d) 10^7 Watch Solution
Let f : R-{3/5}→R be defined by f(x) = (3x+2)/(5x-3) . Then, Watch Solution
