Find the range of each of the following functions. (i) $f(x) = 2 – 3x, x \in \mathbb{R}, x > 0$.

Q.1 Range of the function   ; x ∈ R is 

$A = \{1, 2, 3, 5\}$ and $B = \{4, 6, 9\}$. Define a relation $R$ from $A$ to $B$ by $R = \{(x, y): \text{the difference between } x \text{ and } y \text{ is odd}; x \in A, y \in B\}$. Write $R$ in roster form.

A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (ii) $f(7)$

The function ‘$t$’ which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by $t(C) = \frac{9C}{5} + 32$. Find (iv) The value of $C$, when $t(C) = 212$.

Let $A =\{1,2,3,4\}$, $B = \{1,5,9,11,15,16\}$ and $f = \{(1,5), (2,9), (3,1), (4,5), (2,11)\}$. Are the following true? (ii) $f$ is a function from $A$ to $B$. Justify your answer in each case.

A function $f$ is defined by $f(x) = 2x –5$. Write down the values of (iii) $f(–3)$

Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (ii) \{(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)\}

The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (i) in set-builder form. What is its domain and range?

The Fig2.7 shows a relationship between the sets $P$ and $Q$. Write this relation (ii) roster form. What is its domain and range?

The relation $f$ is defined by $f(x) = \begin{cases} x^2, & 0 \le x \le 3 \\ 3x, & 3 \le x \le 10 \end{cases}$. The relation $g$ is defined by $g(x) = \begin{cases} x^2, & 0 \le x \le 2 \\ 3x, & 2 \le x \le 10 \end{cases}$. Show that $f$ is a function and $g$ is not a function.

Find the range of each of the following functions. (iii) $f(x) = x$, $x$ is a real number.

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (ii) Find the domain of $R$.

If $G = \{7, 8\}$ and $H = \{5, 4, 2\}$, find $G \times H$ and $H \times G$.

Let $f, g : \mathbb{R} \to \mathbb{R}$ be defined, respectively by $f(x) = x + 1$, $g(x) = 2x – 3$. Find $f + g$, $f – g$ and $\frac{f}{g}$.

Let $A = \{9,10,11,12,13\}$ and let $f : A \to \mathbb{N}$ be defined by $f(n) = \text{the highest prime factor of } n$. Find the range of $f$.

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (iii) Find the range of $R$.

Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $\{(a, b): a, b \in A, b \text{ is exactly divisible by } a\}$. (i) Write $R$ in roster form.

Find the domain and the range of the real function $f$ defined by $f(x) = |x – 1|$.

If $f(x) = x^2$, find $\frac{f(1.1) - f(1)}{1.1 - 1}$.