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Home » 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.
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.
CBSE | Class 11 | Excercise 3A | Functions | Maths | RS Aggarwal
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, ∞)

  • 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, ∞)

  • 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)

i

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