RELATIONS AND FUNCTIONS

Function f: R → R by y = f (x) = c, x ∈ R ,Here domain of f is R and its range is {c}
1. Identity function
2. Constant function
3. Polynomial function
4. Rational functions
Let R be the set of real numbers. The real valued function f : R → R by y = f(x) = x for each x ∈ R
1. Identity function
2. Constant function
3. Polynomial function
4. Rational functions
A function f : R → R is said to be polynomial function if for each x in R, y = f (x) = a₀ + a₁x + a₂x² + ...+ an xⁿ, where n is a non-negative integer
1. Identity function
2. Constant function
3. Polynomial function
4. Rational functions
Find x if gff(x) = fgg(x), given f(x) = 3x+1 and g(x) =x+3 .
1. 1
2. 4
3. 3
4. 2
If f(x) = 3x−3 , g(x) = 2x+k and f o g= g 0 f , then find the value of k
1. 1
2. −1
3. 2
4. -2
Find k if f o f(k)= 5 where f(k) =2k−1.
1. 2
2. 1
3. 3
4. 5
If A = {1,3,5} and B = {2,3} then (i) find A×B
1. {(1,2), (1,3), (3,2), (3,3), (5,2), (5,3)}
2. {(2,1), (2,3), (2,5), (3,1), (3,3), (3,5)}
3. {1,3,5}
4. None
If n(A) = p and n(B) = q, then n(A × B) = ?
1. p
2. pq
3. q
4. None
For functions f : X → R and g : X → R, we have (f + g) (x) =?
1. f (x) + g(x), x ∈ X
2. f (x) – g(x), x ∈ X
3. f (x) .g (x), x ∈ X
4. k ( f (x) ), x ∈ X, where k is a real number
For functions f : X → R and g : X → R, we have (f.g) (x) =?
1. f (x) + g(x), x ∈ X
2. f (x) – g(x), x ∈ X
3. f (x) .g (x), x ∈ X
4. k ( f (x) ), x ∈ X, where k is a real number
For functions f : X → R and g : X → R, we have (kf) (x) =?
1. f (x) + g(x), x ∈ X
2. f (x) – g(x), x ∈ X
3. f (x) .g (x), x ∈ X
4. k ( f (x) ), x ∈ X, where k is a real number
For functions f : X → R and g : X → R, we have (f – g) (x) =?
1. f (x) + g(x), x ∈ X
2. f (x) – g(x), x ∈ X
3. f (x) .g (x), x ∈ X
4. k ( f (x) ), x ∈ X, where k is a real number
If (x + 1, y – 2) = (3,1), find the values of x and y
1. 3,1
2. 2,3
3. 3,2
4. None
Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find A × (B ∩ C)
1. {(1,4), (2,4), (3,4)}
2. {(1, 4), (2, 4)}
3. {(1,3), (1,4), (1,5), (1,6), (2,3), (2,4),(2,5), (2,6), (3,3),(3,4), (3,5), (3,6)}
4. None
Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find A × (B ∪ C)
1. {(1,4), (2,4), (3,4)}
2. {(2, 4), (1, 4)}
3. {(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3),(3,4), (3,5), (3,6)}
4. None
Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find (A × B) ∩ (A × C)
1. {(2,4), (1,4)}
2. {(1, 4), (2, 4), (3, 4)}
3. {(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3),
  (3,4), (3,5), (3,6)}
4. None
Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find (A × B) ∪ (A × C)
1. {(1,4), (2,4), (3,4)}
2. {(2, 4), (3, 4), (0, 4)}
3. {(1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,3),
  (3,4), (3,5), (3,6)}
4. None
If A × B ={(p, q),(p, r), (m, q), (m, r)}, find A and B.
1. {p, q} &
  {m, r}
2. {q, m} &
  {p, r}
3. {q, r} &
  {p, m}
4. {p, m} &
  {q, r}
Let A = {1, 2} and B = {3, 4}. Find the number of relations from A to B.
1. 2³
2. 2⁴
3. {q, r} &
  {p, m}
4. {p, m} &
  {q, r}
Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x).
1. x – 1
2. 2x – 1
3. 2x – 5
4. x – 5
Find the domain of the function f(x)= (x²+3x+5)/(x²−5x+4)
1. {2, 4}
2. {0, 0}
3. {1, 4}
4. {1, 0}
If f (x) = x², find [f(1.1)-f(1)]/(1.1-1)
1. 2
2. 0
3. 1
4. undefined
Find the domain of the function f (x) = (x²+2x+1)⁄(x²-8x+12)
1. {1, 4}
2. {2, 6}
3. {1, 6}
4. All
Let f(x) = x² and g(x) = 2x + 1 be two real functions.Find (f + g) (x)
1. x² + 2x + 1
2. x² + x + 1
3. x² - 2x + 1
4. None
Let f(x) = √x and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (fg) (x)
1. √x
2. x√x
3. x³
4. None

RELATIONS AND FUNCTIONS

Quiz