The number of integral values of x in the domain of function / defined as
f(x) Vin (In all-21-x-10 is :
Answers
Given : √(ln | ln | x | |)+ √(7|x| - |x|² - 10)
To Find : The number of integral values of x in the domain of function
Solution:
√ln | ln | x | |
ln 0 is not defines hence x ≠ 0
x = - 1 , or 1 => ln | x | = 0
Hence x can not be - 1 , 1 x ≠ - 1 , 1
root of negative not defined
Hence | ln | x | | > 1 =>
=> ln | x | | < - 1 or ln | x | > 1
=> x < -e or x > e
as e ≈ 2.7183
=> x ≤ - 3 or x ≥ 3 for integral values
√7|x| - |x|² - 10
|x|² = x²
Hence 7x - x² - 10 ≥ 0 if x ≥ 0
or -7x - x² - 10 ≥ 0 if x < 0
7x - x² - 10
=> -x² + 5x + 2x - 10
=> - ( x - 5)(x - 2) ≥ 0
=> ( x - 5)(x - 2) ≤ 0
=> 2 ≤ x ≤ 5
-7x - x² - 10 ≥ 0
=> x² + 7x + 10 ≤ 0
=> (x + 5)(x + 2) ≤ 0
-5 ≤ x ≤ -2
x ≤ - 3 or x ≥ 3
-5 ≤ x ≤ -2 or 2 ≤ x ≤ 5
combining both
x = -5 , - 4 , - 3 , 3 , 4 , 5
Hence there are 6 integral values
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