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.
(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)