we have
[tex]f(x)=\frac{1}{\sqrt{x+10}}[/tex]
we know that
the denominator can not be equal to zero and the term inside the square root can't be negative.
so
[tex](x+10) > 0\\x > -10[/tex]
the domain is the interval--------> (-10,∞)
-10 < x < ∞
the range is the interval------> (0,∞)
0 < f(x) < ∞
using a graphing tool
see the attached figure
Statements
A. Its domain is (-∞,0] and its range is (0,∞)
The statement is false
B. Its domain is(-10,∞) and its range is(0,∞)
The statement is true
C. Its domain is(-10, ∞)and its range is(-∞,∞)
The statement is false
D. Its domain is[-10,∞) and its range is (-∞,0) U (0,∞)
The statement is false
