1. Two marks example problems

1. Let \(X = \{1\), \(2\), \(3\), \(4\}\) and \(Y = \{2\), \(4\), \(6\), \(8\), \(10\}\) and \(\mathbb{R} = \{(1, 2)\), \((2, 4)\), \((3, 6)\), \((4, 8)\}\). Show that \(\mathbb{R}\) is a function and find its domain, co-domain, and range?

 

\(\mathbb{R}\) is not a functiona function.

 

Domain \(=\) $\left\{i,i,i,i\right\}$

 

Co-domain \(=\) $\left\{i,i,i,i,i\right\}$

 

Range \(=\) $\left\{i,i,i,i\right\}$

 

 

2. A relation '\(f\)' is defined as \(f(x) = x^2 - 2\) where, \(x \in \{\)−2, −1 ,0, 3\(\}\).

 

(i) List the elements of '\(f\)'.

 

The elements of '\(f\)' are \(\{(\), \()\), \((\), \()\), \((\), \()\), \((\), \()\}\)

 

[Note: Enter the elements in ascending order of the preimages]

 

 

(ii) Is \(f\) a function?

 

\(f\) is a functionnot a function