Chapter 2
3sin-1 x = sin -1 (3x - 4 x3), 1 1- ,2 2x ∈
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 - 2x - 8 (ii) 4 s2 - 4s + 1 (iii) 6x2 - 3 - 7x (iv) 4 u2 + 8u (v) t2 - 15 (vi) 3x2 - x - 4
Let A = {1, 2, 3,...,14}. Define a relation R from A to A by R = {(x, y) : 3x - y = 0, where x, y ∈ A}. Write down its domain, codomain and range.
3cos-1 x = cos -1 (4x3 - 3x), 1 , 12x ∈ Write the following functions in the simplest form: 3. 1 1 1tan x x − + − , x ≠ 0 4. 1 1 costan 1 cos x x − − + , 0 < x < π
Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural number less than 4; x, y ∈N}. Depict this relationship using roster form. Write down the domain and the range.
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) (ii) (iii)
(iv) (v) (vi)
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
The Fig2.7 shows a relationship between the sets P and Q. Write this relation (i) in set-builder form (ii) roster form. What is its domain and range?
1 cos sintan cos sin / x x / x x − − + , 4 −π < x < 3 π 6. 2 2 tan x a x − − , |x| < a 7. 2 3 3 2 3tan
| a | x | x |
|---|---|---|
| a ax − − − , a > 0; 3 3 − < <a a x Find the values of each of the following: 8. -1 -1 1tan 2cos 2sin 2 9. -1 -1 2 2 1 2 1tan sin cos² 1 1 x y x y −+ + + , | x | < 1, y > 0 and xy < 1 Find the values of each of the expressions in Exercises 16 to 18. 10. -1 2sin sin 3 π 11. -1 3tan tan 4 π 12. -1 -13 3tan sin cot5 2 + 13. 1 7cos cos is equal to6 − π |
(A) 7 / π (B) 5 / π (C) 3 / π (D) 6 π 14. 1 1sin sin ( )3 2 −π − − is equal to (A) 1 / 2 (B) 1 / 3 (C) 1 / 4 (D) 1 15. 1 1tan 3 cot ( 3)− −− − is equal to (A) π (B) 2 / π− (C) 0 (D) 2 3
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a , b ∈A, b is exactly divisible by a}. (i) Write R in roster form (ii) Find the domain of R (iii) Find the range of R.
Determine the domain and range of the relation R defined by R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}.
Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a - b is an integer}. Find the domain and range of R.