The Total solution for NCERT class 6-12
Find the domain of definition of f(x) = cos -1 (x2 –4)
Answer 1 :
Given f(x) = cos -1 (x2 –4)
We know that domain ofcos-1 (x2 – 4) lies in the interval [-1, 1]
Therefore, we canwrite as
-1 ≤ x2 –4 ≤ 1
4 – 1 ≤ x2 ≤1 + 4
3 ≤ x2 ≤5
±√ 3 ≤ x ≤ ±√5
– √5 ≤ x ≤ – √3 and √3≤ x ≤ √5
Therefore domain ofcos-1 (x2 – 4) is [- √5, – √3] ∪ [√3, √5]
Find the domain of f(x) = cos-1 2x + sin-1 x.
Answer 2 :
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]
Find the domain of f(x) = cos-1x + cos x.
Answer 3 :
Answer 4 :
Find the principalvalue of each of the following :
Answer 5 :
Answer 6 :
Answer 7 :
Answer 8 :