Q. 185.0( 3 Votes )

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 :

(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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