Question

Find the domain of cos^–1 (3x – 2).

Answer 1

For cos^–1 a

Domain = All possible values of a = [−1, 1]

Range = All possible values of cos^–1 a = [0, π]

Now, the domain of cos^–1 (3x – 2) is −1 ≤ 3x − 2 ≤ 1.

We are adding 2 to both sides of the equation.

−1 + 2 ≤ 3x − 2  + 2 ≤ 1 + 2

1 ≤ 3x ≤ 3

Divide by 3 on all sides.

`1/3 ≤ (3x)/3 ≤ 3/3`

`1/3 ≤ x ≤ 1`

Thus, the domain is `[1/3,1]`.