If the domain of the function `f(x) = sqrt(3 cos^(-1) (4x) - pi)` is `[a, b]`, then the value of `(4a + 64b)` is ___

Answer

7

Explanation

`f(x) = sqrt(3 cos^(-1) (4x) -pi)` is defined ltbr. If `cos^(-1) 4x ge (pi)/(3) rArr 4x le (1)/(2) " or " x le (1)/(8)`
Also, `-1 le 4x 1 " or " (-1)/(4) le x le (1)/(4)`
Therefore, from Eqs. (i) and (ii) we have domain , `x in [(-1)/(4) , (1)/(8)]`
`rArr 4a + 64b = 7`