Answer:
For f(x) = √(2·x + 2) - √(x + 18), at f(x) = -1 the possible x-values includes;
-0.757, -17.5
Step-by-step explanation:
Given that the function is f(x) = √(2·x + 2) - √(x + 18)
The value of 'x' when f(x) = -1, is given as follows;
-1 = √(2·x + 2) - √(x + 18)
-1² = (√(2·x + 2) - √(x + 18))² = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)
1 = 3·x + 20 - 2·√(2·x + 2)×√(x + 18)
2·√(2·x + 2)×√(x + 18) = 3·x + 20 - 1 = 3·x + 19
2·x² + 38·x + 36 = (3·x + 19)/2
2·x² + 38·x + 36 - (3·x + 19)/2 = 0
4·x² + 73·x + 53 = 0
From which we get;
x = (-73 ± √(73² - 4 × 4 × 53))/(2 × 4)
x ≈ -0.757, and x ≈ -17.5
