Let the domains of the functions f(x)= log ₁₀ log ₁₀ (8- log ₂(x²+4x+5)) and g(x)= sin ⁻¹ ((7x+10)/(x-2)) be (α,β) and [γ,δ], respectively. Then α²+β²+γ²+δ² is equal to:

Sets, Relations and Functions: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q108

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let the domains of the functions

f(x)=\log_{10}\log_{10}\bigl(8-\log_{2}(x^2+4x+5)\bigr)

and

g(x)=\sin^{-1}\!\bigl(\tfrac{7x+10}{x-2}\bigr)

(\alpha,\beta)

and

[\gamma,\delta]

, respectively. Then

\alpha^2+\beta^2+\gamma^2+\delta^2

is equal to:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q108

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumSets, Relations and Functions168× since 2002

Let the domains of the functions

f(x)=\log_{10}\log_{10}\bigl(8-\log_{2}(x^2+4x+5)\bigr)

and

g(x)=\sin^{-1}\!\bigl(\tfrac{7x+10}{x-2}\bigr)

(\alpha,\beta)

and

[\gamma,\delta]

, respectively. Then

\alpha^2+\beta^2+\gamma^2+\delta^2

is equal to: