Question -
Answer -
Given that f(x) = cos-1 2x+ sin-1 x.
Now we have to findthe domain of f(x),
We know that domain ofcos-1 x lies in the interval [-1, 1]
Also know that domainof sin-1 x lies in the interval [-1, 1]
Therefore, the domainof cos-1 (2x) lies in the interval [-1, 1]
Hence we can write as,
-1 ≤ 2x ≤ 1
– ½ ≤ x ≤ ½
Hence, domain of cos-1(2x)+ sin-1 x lies in the interval [- ½, ½]