Five marks example problems — task. Mathematics State Board, Class 10.

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1. If \(X = \{-5, 1, 3, 4\}\) and \(Y = \{a, b, c\}\), then which of the following relations are functions from \(X\) to \(Y\)?

(i) \(\mathbb{R}_1 = \{(-5, a), (1, a), (3, b)\}\)

(ii) \(\mathbb{R}_2 = \{(-5, b), (1, b), (3, a), (4, c)\}\)

(iii) \(\mathbb{R}_3 = \{(-5, a), (1, a), (3, b), (4, c), (1, b)\}\)

2. Given \(f(x) = 2x - x^2\), find:

(i) \(f(1)\) \(=\)

i

(ii) \(f(x + 1)\) \(=\)

- i^{i} + i

(iii) \(f(x) + f(1)\) \(=\)

- i^{i} + i i + i

[Note: Enter the coefficients and variables in separate boxes.]

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5. Five marks example problems