If the domain of the function f ( x ) = x 2 - 16 x 2 - 4 + log 10 ( x 2 + 3 x - 10 ) is ( - , p ) [ q , ) then p 2 + q =

Question

If the domain of the function $f (x) = \frac{\sqrt{x^{2} - 16}}{x^{2} - 4} + \log_{10} (x^{2} + 3 x - 10)$ is $(- \infty, p) \cup [q, \infty)$ then $p^{2} + q =$ ________

Smart Achievers · Accepted Answer

(2)

$x^{2} - 16 \geq 0, x \neq 2, - 2, (x + 5) (x - 2) \geq 0$

$x \in (- \infty, - 5) \cup (2, \infty)$

Solution

Q.
If the domain of the function $f (x) = \frac{\sqrt{x^{2} - 16}}{x^{2} - 4} + \log_{10} (x^{2} + 3 x - 10)$ is $(- \infty, p) \cup [q, \infty)$ then $p^{2} + q =$ ________

1 21

2 29

3 17

4 34

Ans.
(2)

$x^{2} - 16 \geq 0, x \neq 2, - 2, (x + 5) (x - 2) \geq 0$

$x \in (- \infty, - 5) \cup (2, \infty)$

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