Find the domain of definition of the function
 

a) (−2, 1)

b) (−2, 1) and x ≠ 0

c) (0, 1)

d) (−2, 2)

Find the domain of definition of the function
 

a)

b)

c)

d) ; where k = 0, ±1, ±2, ...

Find the domain of definition of the function
 

a) (−∞, ∞)

b) (−∞, 0)

c) (0, ∞)

d) (−∞, 0) ∪ (0, ∞)

Find the domain of definition of the function
 

a) (1, 2)

b) [1, 2]

c) (1, 2]

d) [1, 2)

Find the domain of definition of the function
  to be defined

a) (0, 4)

b) (4, ∞)

c) (0, ∞)

d) (−4, 4)

Find the domain of definition of the function
 

a) (−∞, 0)

b) (0, ∞)

c) (−∞, ∞)

d) Not defined for any x

Find the domain of definition of the function
 

a) (−∞, ∞)

b) (−∞, −2)

c) (2, ∞)

d) (−∞, −2) ∪ (−2, 2) ∪ (2, ∞)

Find the domain of definition of the function
 

a) (−1, 1)

b) (−∞, −1)

c) (1, ∞)

d) {−1, 1}

Find the range of the function
 

a)

b)

c)

d) [0, ∞)

Find the range of the function
 

a)

b)

c)

d) (−∞, ∞)

Solve the equation
 

a) x = 0

b) x = 1

c) x = −1

d) x = −1, 0

Find domain of definition of the function
 

a) (3, 4)

b) (3, 4]

c) [−4, 4]

d) (3, 3 + π)

Find domain of definition of the function
 

a) [−1, 5]

b) (−∞, 3]

c) [−1, 3]

d) [3, 5]

Find domain of definition of the function
 

a) (−∞, −1)

b) (−1, 1)

c) (1, ∞)

d) (−1, ∞)

If the function f (x) is defined on the interval [0, 1] what is the domain of  f (x − 5)

a) [0, 5]

b) [0, 6]

c) [5, 6]

d) (6, ∞)

If the function f (x) is defined on the interval [0, 1] what is the domain of  f (tanx)

a) 0 < x < kπ ; k

b)  ; k

c)  ; k

d)   ; k

Prove that the function f (x) =   is not a periodic one.

Is the following function even or odd
f (x) =

a) Even

b) Odd

c) Cannot say

d) Neither odd nor even

Is the following function even or odd
f (x) =

a) Even

b) Odd

c) Cannot say

d) Neither odd nor even

Prove that the following function
f (x) = x + sinx
is non-periodic

Prove that the following function
 
is non-periodic

Prove the inequality
 

Prove the inequality