Example 9 Q 9 The domain of y = cos-1 1-2x4 is (a) -32, 52 (b) -1, - Maths - Sets

Question

Example 9
Q 9 The domain of y = cos - 1   1 - 2 x 4 is
(a) - 3 2 ,   5 2
(b) - 1 ,   1
(c) 0 ,   2
(d) - 1 2 ,   3 2
Ans (a)

Neha Sethi · Accepted Answer

Dear student
We have, y=cos-11-2x4The domain of  a function  is the set of input  for which function is realand defined
Finding known functions domain restrictions:cos-1fx⇒-1≤fx≤1Solving ,-1≤1-2x4≤1So, we have -1≤1-2x4 and 1-2x4≤1Consider, -1≤1-2x4-4≤1-2x⇒2x≤1+4⇒x≤52and 1-2x4≤1⇒1-2x≤4⇒-3≤2x⇒x≥-32Combine the ranges , we get-32≤x≤52Interval Notation:-32,52
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Example 9 Q.9. The domain of y = cos - 1 1 - 2 x 4 is (a) - 3 2 , 5 2 (b) - 1 , 1 (c) 0 , 2 (d) - 1 2 , 3 2 Ans. (a)

Example 9
Q.9. The domain of y = $\cos^{- 1} \frac{1 - 2 x}{4}$ is
(a) $[- \frac{3}{2}, \frac{5}{2}]$
(b) $[- 1, 1]$
(c) $[0, 2]$
(d) $[- \frac{1}{2}, \frac{3}{2}]$
Ans. (a)