Mark (√) against the correct answer in the following: Let f(x) = co

1.	Mark (√) against the correct answer in the following: Let f(x) = cos-1(3x – 1). Then, dom (f) = ?A. \((0, \frac{2}{3})\)B. \([0,\frac{2}{3}]\)C. \([\frac{-2}{3},\frac{2}{3}]\)D. None of these
Answer» Correct Answer is (B) \([0,\frac{2}{3}]\) f(x) = cos^-1(3x - 1). domain of cos^-1x = [ - 1,1] on multiplying by an integer the domain decreases by same number ⇒ domain of cos^-13x = [ - 1/3,1/3] ⇒ domain of cos^-1 (3x - 1) = [1/3 - 1/3,1/3 + 1/3] = [0,2/3]

Mark (√) against the correct answer in the following: Let f(x) = cos-1(3x – 1). Then, dom (f) = ?A. \((0, \frac{2}{3})\)B. \([0,\frac{2}{3}]\)C. \([\frac{-2}{3},\frac{2}{3}]\)D. None of these

Answer»

Correct Answer is (B) \([0,\frac{2}{3}]\)

f(x) = cos^-1(3x - 1).

domain of cos^-1x = [ - 1,1]

on multiplying by an integer the domain decreases by same number

⇒ domain of cos^-13x = [ - 1/3,1/3]

⇒ domain of cos^-1 (3x - 1) = [1/3 - 1/3,1/3 + 1/3] = [0,2/3]