Find the range of the following functions: x - 1

To find:- Range of x - 1 Let f x = x - 1 f x is defined when x - 1 ≥ 0 ∴ Domain of f x = [ 1 , ∞ ) As, range of x = [ 0 , ∞ ) ∴ Range of x - 1 = [ 0 , ∞ )

Find the range of the following functions: x - 1

To find:- Range of x - 1 Let f x = x - 1 f x is defined when x - 1 ≥ 0 ∴ Domain of f x = [ 1 , ∞ ) As, range of x = [ 0 , ∞ ) ∴ Range of x - 1 = [ 0 , ∞ )

Find the range of the following functions: x 1 - x

To find range of x 1 - x Here, domain is R - 1 . Let y = x 1 - x ⇒ y - x y = x ⇒ y = x + x y ⇒ x 1 + y = y ⇒ x = y 1 + y ∴ y can take all real values except - 1 ∴ Range of x 1 - x is R - - 1 or - ∞ , ∞ - - 1

Find the range of the following functions: 1 2 - cos 3 x

To find:- range of 1 2 - cos 3 x As, - 1 ≤ cos 3 x ≤ 1 ⇒ 1 ≥ - cos 3 x ≥ - 1 ⇒ - 1 ≤ - cos 3 x ≤ 1 ⇒ 2 - 1 ≤ 2 - cos 3 x ≤ 3 ⇒ 1 ≤ 2 - cos 3 x ≤ 3 ⇒ 1 1 ≥ 1 2 - cos 3 x ≥ 1 3 ∴ Range of 1 2 - cos 3 x = 1 3 , 1