Question

. f, g and h are three functions defined from R to R as following:
(i) f(x) = x2
(ii) g(x) = x2 + 1
(iii) h(x) = sin x
That, find the range of each function.

Answer 1

(i) f: R → R such that f(x) = x2

Since the value of x is squared, f(x) will always be equal or greater than 0.

∴ the range is [0, ∞)

$\:$

(ii) g: R → R such that g(x) = x2 + 1

Since, the value of x is squared and also adding with 1, g(x) will always be equal or

greater than 1.

∴ Range of g(x) = [1, ∞)

$\:$

(iii) h: R → R such that h(x) = sin x

We know that, sin (x) always lies between -1 to 1

∴ Range of h(x) = (-1, 1)

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