If the domain of the function f x = sec - 1 2 x 5 x + 3 is [ α , β ) ∪ ( γ , δ ] , then 3 α + 10 β + γ + 21 δ is equal to __________

Step-by-step solution

We know that, Domain of sec - 1 x is ( - ∞ , - 1 ] ∪ [ 1 , ∞ ) . Now, f x = sec - 1 2 x 5 x + 3 So, 2 x 5 x + 3 ≤ - 1   or   2 x 5 x + 3 ≥ 1 ⇒ 2 x 5 x + 3 + 1 ≤ 0   or   2 x 5 x + 3 - 1 ≥ 0 ⇒ 7 x + 3 5 x + 3 ≤ 0   or   - 3 x - 3 5 x + 3 ≥ 0 ⇒ 7 x + 3 5 x + 3 ≤ 0   or   x + 1 5 x + 3 ≤ 0 ⇒ x ∈ [ - 1 , - 3 5 ) ∪ ( - 3 5 , - 3 7 ] So, α = - 1 ,   β = - 3 5 , &#160