10th Maths Unit 1: Relation and Function Exercise Problems with Solutions

Exercise: Relation and Function - Problems & Solutions

UNIT EXERCISE

Question 1

If the ordered pairs \( (x^2 - 3x, y^2 + 4y) \) and (-2, 5) are equal, then find \(x\) and \(y\).

Question 2

The cartesian product \(A \times A\) has 9 elements among which (–1, 0) and (0,1) are found. Find the set A and the remaining elements of \(A \times A\).

Question 3

Given that \(f(x)\) =

(i) \(f(0)\)

(ii) \(f(3)\)

(iii) \(f(a + 1)\) in terms of \(a\). (Given that \(a \ge 0\))

Question 4

Let A = {9,10,11,12,13,14,15,16,17} and let \(f: A \to N\) be defined by \(f(n)\) = the highest prime factor of \(n \in A\). Write f as a set of ordered pairs and find the range of f.

Question 5

Find the domain of the function \( f(x) = \sqrt{1+\sqrt{1-\sqrt{1-x^2}}} \)

Question 6

If \(f(x) = x^2\), \(g(x) = 3x\) and \(h(x) = x - 2\), Prove that \((f \circ g) \circ h = f \circ (g \circ h)\).

Question 7

Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify whether \(A \times C\) is a subset of \(B \times D\).

Question 8

If \(f(x) = \frac{x-1}{x+1}, x \neq -1\) show that \(f(f(x)) = -\frac{1}{x}\) provided \(x \neq 0\).

Question 9

The functions f and g are defined by \(f(x) = 6x + 8\); \(g(x) = \frac{x-2}{3}\).

(i). Calculate the value of \(gg(\frac{1}{2})\)

(ii) Write an expression for \(gf(x)\) in its simplest form.

Question 10

Write the domain of the following real functions:

(iv) \(h(x) = x + 6\)

Answers

1. 1,2 and -5, 1
2. {-1, 0, 1} , {(-1, -1),(-1, 1),(0, -1),(0, 0),(1, -1),(1, 0),(1, 1)}
3. (i) 4 (ii) \(\sqrt{2}\) (iii) \(\sqrt{a}\)
4. {(9, 3),(10, 5),(11, 11),(12, 3),(13, 13),(14, 7),(15, 5),(16, 2),(17, 17)} , {2,3,5,11,13,17}
5. {–1, 0, 1}
6. (i) -5/6 (ii) 2(x + 1)
7. (i) R - {9} (ii) R (iii) [2, ∞) (iv) R