Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}
(iii) {(1,3), (1,5), (2,5)}
(i) Yes, Domain = \(\{2, 5, 8, 11, 14, 17\}\), Range = \(\{1\}\)
(ii) Yes, Domain = \(\{2, 4, 6, 8, 10, 12, 14\}\), Range = \(\{1, 2, 3, 4, 5, 6, 7\}\)
(iii) No.
Find the domain and range of the following real functions:
(i) \(f(x) = -|x|\)
(ii) \(f(x) = \sqrt{9 - x^2}\)
(i) Domain = \(\mathbb{R}\), Range = \(( -\infty, 0 ]\)
(ii) Domain = \(\{x : -3 \le x \le 3\}\), Range = \(\{x : 0 \le x \le 3\}\)
A function \(f\) is defined by \(f(x) = 2x - 5\). Write the values of:
(i) \(f(0)\)
(ii) \(f(7)\)
(iii) \(f(-3)\)
(i) \(f(0) = -5\)
(ii) \(f(7) = 9\)
(iii) \(f(-3) = -11\)
The function \(t\) which maps temperature in degree Celsius into degree Fahrenheit is defined by
\[ t(C) = \dfrac{9C}{5} + 32. \]
Find:
(i) \(t(0)\)
(ii) \(t(28)\)
(iii) \(t(-10)\)
(iv) The value of \(C\) when \(t(C)=212\)
(i) 32
(ii) \(\dfrac{412}{5}\)
(iii) 14
(iv) 100
Find the range of each of the following functions.
(i) \(f(x) = 2 - 3x, \ x \in \mathbb{R}, x > 0\)
(ii) \(f(x) = x^2 + 2, x\) is a real number
(iii) \(f(x) = x, x\) is a real number
(i) Range = \(( -\infty, 2 )\)
(ii) Range = \([2, \infty)\)
(iii) Range = \(\mathbb{R}\)