Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2(2 - 6\log_{27}(2x+5))$ be $(\gamma, \delta)$. Then $|7(\alpha + \beta) + 4(\gamma + \delta)|$ is equal to __________

JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

Let the domain of the function

f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)

[\alpha, \beta]

and the domain of

g(x) = \log_2(2 - 6\log_{27}(2x+5))

(\gamma, \delta)

. Then

|7(\alpha + \beta) + 4(\gamma + \delta)|

is equal to __________

Official answer

NTA final key.