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Question

f, g, h are three function defined from R to R as follows:

(i) f(x) = x2
(ii) g(x) = sin x
(iii) h(x) = x2 + 1

Find the range of each function.

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Solution

(i) Given:
f (x) = x2
Range of f(x) = R+ (set of all positive integers)
= {y ∈ R| y ≥ 0}
(ii) Given:
g(x) = sin x
Range of g(x) = {y ∈ R : -1 ≤ y ≤ 1}

(iii) Given:
h (x) = x2 + 1
Range of h (x) = {y ∈ R : y ≥ 1}

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