The problem describes a linear function $f$ such that $f(7) = 14$. The tasks are: (a) Determine the expression of $f(x)$. (b) Find the number $a$ such that $f(a) = 21$. (c) Draw the line (D), which is the graphical representation of the function $f$.

1. Problem Description

The problem describes a linear function $f$ such that $f(7) = 14$. The tasks are:

(a) Determine the expression of $f(x)$.

(b) Find the number $a$ such that $f(a) = 21$.

(c) Draw the line (D), which is the graphical representation of the function $f$.

2. Solution Steps

(a) Since $f$ is a linear function, we can write it in the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Given that $f(7) = 14$, we have $7m + b = 14$.

However, since the prompt states that $f$ is a "linear function," it's possible the problem is supposed to read "linear FUNCTION."

Assuming that $f$ is a linear function means we can assume $b = 0$, so $f(x) = mx$.

Then, $f(7) = 7m = 14$, which implies $m = \frac{14}{7} = 2$.

Therefore, $f(x) = 2x$.

(b) We want to find $a$ such that $f(a) = 21$.

Since $f(x) = 2x$, we have $f(a) = 2a = 21$.

Solving for $a$, we get $a = \frac{21}{2} = 10.5$.

(c) To draw the graph of $f(x) = 2x$, we can find two points on the line.

When $x = 0$, $f(0) = 2(0) = 0$, so the point $(0, 0)$ is on the line.

When $x = 1$, $f(1) = 2(1) = 2$, so the point $(1, 2)$ is on the line.

The line (D) passes through the points $(0, 0)$ and $(1, 2)$.

3. Final Answer

(a) $f(x) = 2x$

(b) $a = 10.5$

(c) The graph of $f(x) = 2x$ is a straight line passing through (0,0) and (1,2).