jee-main 2024 Q72

jee-main · India · session1_01feb_shift2 Composite & Inverse Functions Determine Domain or Range of a Composite Function
If the domain of the function $f(x) = \frac{\sqrt{x^2 - 25}}{4 - x^2} + \log_{10}(x^2 + 2x - 15)$ is $(-\infty, \alpha) \cup (\beta, \infty)$, then $\alpha^2 + \beta^3$ is equal to:
(1) 140
(2) 175
(3) 150
(4) 125
If the domain of the function $f(x) = \frac{\sqrt{x^2 - 25}}{4 - x^2} + \log_{10}(x^2 + 2x - 15)$ is $(-\infty, \alpha) \cup (\beta, \infty)$, then $\alpha^2 + \beta^3$ is equal to:\\
(1) 140\\
(2) 175\\
(3) 150\\
(4) 125