Question

For what values of x is the expression below defined?

√x+5+√1-x
A. -5 OB. 5> x≤-1
C. 5>x>1
D. 5≤x≤1

Answer 1

The expression √x+5+√1-x is defined for all values of x such that the value under the square root sign is non-negative. We can find the values of x that satisfy this condition by considering each of the square roots separately.

For the first square root, the value under the square root must be non-negative, so we have the following inequality:

x + 5 ≥ 0

x ≥ -5

For the second square root, the value under the square root must be non-negative, so we have the following inequality:

1 - x ≥ 0

x ≤ 1

Therefore, the expression is defined for all values of x that satisfy both of these inequalities. This means that the expression is defined for values of x in the range -5 ≤ x ≤ 1. The correct answer is therefore option D.