f, g and h are three functions defined from R to R as following: (i)

1.	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)

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)