Find the domain of f(x) = cos-1 2x + sin-1 x.

1.	Find the domain of f(x) = cos-1 2x + sin-1 x.
Answer» Given f(x) = cos^-1 2x + sin^-1 x. Let us find the domain of f(x), As we know domain of cos^-1 x lies in the interval [-1, 1] Also know that domain of sin^-1 x lies in the interval [-1, 1] So, the domain of cos^-1(2x) lies in the interval [-1, 1] Thus, we can write, -1 ≤ 2x ≤ 1 – (1/2) ≤ x ≤ (1/2) Thus, domain cos^-1(2x) + sin^-1x lies in the interval [-(1/2), (1/2)]

Answer»

Given f(x) = cos^-1 2x + sin^-1 x.

Let us find the domain of f(x),

As we know domain of cos^-1 x lies in the interval [-1, 1]

Also know that domain of sin^-1 x lies in the interval [-1, 1]

So, the domain of cos^-1(2x) lies in the interval [-1, 1]

Thus, we can write,

-1 ≤ 2x ≤ 1

– (1/2) ≤ x ≤ (1/2)

Thus, domain cos^-1(2x) + sin^-1x lies in the interval [-(1/2), (1/2)]

Discussion