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Consider the function f(x) = 1/(6 sin x - 8 cos x + 5). Evaluate the following statements: Statement-1: The function has no maximum or minimum value. Statement-2: The function is unbounded.

1. Statement-1 is false and Statement-2 is true
2. Statement-1 is true and Statement-2 is true, and Statement-2 correctly explains Statement-1
3. Statement-1 is true and Statement-2 is true, but Statement-2 does not correctly explain Statement-1
4. Statement-1 is true and Statement-2 is false

Correct answer: Statement-1 is true and Statement-2 is true, and Statement-2 correctly explains Statement-1

Solution

The function is defined as a rational function where the denominator can take values that approach zero, leading to unbounded behavior. Since the function can become infinitely large or small, it does not attain maximum or minimum values, making Statement-1 true and Statement-2 true, with the latter explaining the former.

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