What are the solutions for problems 7, 8, and 9? Problem 7 asks to identify a finite set among given options. Problem 8 requires finding f(2) for f(x) = 4x+2. Problem 9 asks for the range and arrow di

$$f(2) = 10$$

The value of $f(2)$ is $\boxed{10}$.

9. Consider the function $f(x) = 2x$. If the domain is $\{0, 1, 2\}$, find the range values. Hence, draw the arrow diagram.

For $x=0$:

$$f(0) = 2(0) = 0$$

For $x=1$:

$$f(1) = 2(1) = 2$$

For $x=2$:

$$f(2) = 2(2) = 4$$

The range values are $\boxed{\{0, 2, 4\}}$.

Domain: $\{0, 1, 2\}$
Range: $\{0, 2, 4\}$
The arrow diagram shows the mapping from each domain element to its corresponding range element:

$$0 \to 0$$ $$1 \to 2$$ $$2 \to 4$$

10. Out of 17 teachers in a school, 10 teach Economics, and 9 teach Maths. The number of teachers who teach both subjects is twice that of those who teach none of the subjects. Use a Venn diagram to find the numbers that teach:

(a) Both subjects.

(b) None of the subject.

(c) Only one subject.

Let $E$ be the set of teachers who teach Economics and $M$ be the set of teachers who teach Maths.
Total teachers $N = 17$.
Number of teachers teaching Economics, $|E| = 10$.
Number of teachers teaching Maths, $|M| = 9$.

Let $x$ be the number of teachers who teach both subjects, i.e., $x = |E \cap M|$.
Let $y$ be the number of teachers who teach none of the subjects, i.e., $y = |E \cup M|'$.

From the problem statement, the number of teachers who teach both subjects is twice that of those who teach none:

$$x = 2y$$

The number of teachers who teach only Economics is $|E| - x = 10 - x$.
The number of teachers who teach only Maths is $|M| - x = 9 - x$.

The total number of teachers is the sum of those who teach only Economics, only Maths, both, and none:

$$(10 - x) + (9 - x) + x + y = 17$$

$$19 - (2y) + y = 17$$ $$19 - y = 17$$

$$y = 19 - 17$$ $$y = 2$$

So, the number of teachers who teach none of the subjects is 2.

$$x = 2(2)$$ $$x = 4$$

So, the number of teachers who teach both subjects is 4.

Number of teachers who teach only Economics $= 10 - x = 10 - 4 = 6$.
Number of teachers who teach only Maths $= 9 - x = 9 - 4 = 5$.
Number of teachers who teach only one subject $= 6 + 5 = 11$.

The answers are:

(a) Both subjects: $\boxed{4}$

(b) None of the subject: $\boxed{2}$

(c) Only one subject: $\boxed{11}$