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Determine the range of each function: (i) f(x) = 2^(x²) + 1; (ii) f(x) = 1/(8 - 3*sin x).

1. (i) [2, infinity) (ii) [1/11, 1/5]
2. (i) (1, infinity) (ii) (1/11, 1/5)
3. (i) [1, infinity) (ii) [1/5, 1/11]
4. (i) [2, infinity) (ii) [1/8, 1/5]

Correct answer: (i) [2, infinity) (ii) [1/11, 1/5]

Solution

In (i) the exponent x² is at least 0 so the power is at least 1. In (ii) the denominator runs over [5, 11], and the reciprocal is a decreasing map, so the function's range is the reciprocal interval.

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