The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. It includes all the values that can be substituted into the function without causing any undefined behavior such as division by zero or taking the square root of a negative number.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions focuses on the inverse of trigonometric functions like sine and cosine and tangent or cosecant and secant and cotangent. It explains how to find angles when the value of a trigonometric function is given. The chapter includes domains and ranges graphs and solving equations involving inverse trigonometric functions.
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Let us now solve this function step by step to find out the domain of sin⁻¹(3x – 1).
Step 1: Domain of sin⁻¹(y)
We know that sin⁻¹(y) is defined only if -1 ≤ y ≤ 1.
In the case of sin⁻¹(3x – 1), we must have:
-1 ≤ 3x – 1 ≤ 1
Step 2: Solve the inequality
1. Add 1 to all sides:
0 ≤ 3x ≤ 2
2. Divide through by 3:
0 ≤ x ≤ 2/3
Step 3: Domain
The domain of sin⁻¹(3x – 1) is:
[0, 2/3]
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