We are given two exercises. Exercise 2: $f$ is a linear function such that $f(7) = 14$. We need to: 1. Find the expression of $f(x)$.

1. Problem Description

We are given two exercises.

Exercise 2:

$f$ is a linear function such that $f(7) = 14$. We need to:

1. Find the expression of $f(x)$.

2. Find the number whose image is $21$ by the function $f$.

3. Draw the line $(D)$ representing the graph of the function $f$.

Exercise 3:

$g$ is an affine function such that $g(0) = 3$ and $g(2) = 7$. We need to:

1. Find the expression of $g(x)$.

2. Calculate $g(1)$ and $g(3)$.

3. Find the number whose image is $21$ by the function $g$.

4. Draw the line $(\Delta)$ representing the graph of the function $g$.

2. Solution Steps

Exercise 2:

1. Since $f$ is a linear function, it has the form $f(x) = ax$ for some constant $a$. We are given that $f(7) = 14$. Therefore, $7a = 14$, which implies $a = 2$. Thus, $f(x) = 2x$.

2. We want to find $x$ such that $f(x) = 21$. Thus, $2x = 21$, which implies $x = \frac{21}{2} = 10.5$.

3. The line $(D)$ representing the graph of $f(x) = 2x$ passes through the points $(0, 0)$ and $(7, 14)$. You can draw this line on a graph.

Exercise 3:

1. Since $g$ is an affine function, it has the form $g(x) = ax + b$ for some constants $a$ and $b$. We are given that $g(0) = 3$ and $g(2) = 7$.

Using $g(0) = 3$, we have $a(0) + b = 3$, which implies $b = 3$.

Using $g(2) = 7$, we have $a(2) + b = 7$. Substituting $b = 3$, we get $2a + 3 = 7$, which implies $2a = 4$, so $a = 2$.

Thus, $g(x) = 2x + 3$.

2. We need to calculate $g(1)$ and $g(3)$.

$g(1) = 2(1) + 3 = 2 + 3 = 5$.

$g(3) = 2(3) + 3 = 6 + 3 = 9$.

3. We want to find $x$ such that $g(x) = 21$. Thus, $2x + 3 = 21$, which implies $2x = 18$, so $x = 9$.

4. The line $(\Delta)$ representing the graph of $g(x) = 2x + 3$ passes through the points $(0, 3)$ and $(2, 7)$. You can draw this line on a graph.

3. Final Answer

Exercise 2:

1. $f(x) = 2x$

2. $x = 10.5$

3. Draw the line passing through (0,0) and (7,14).

Exercise 3:

1. $g(x) = 2x + 3$

2. $g(1) = 5$ and $g(3) = 9$

3. $x = 9$

4. Draw the line passing through (0,3) and (2,7).