Q. 185.0( 3 Votes )

# f, g and h are three functions defined from R to R as following:

(i) f(x) = x^{2}

(ii) g(x) = x^{2} + 1

(iii) h(x) = sin x

That, find the range of each function.

Answer :

(i) f: R → R such that f(x) = x^{2}

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) = x^{2} + 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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