Which of the following is true about the function below? 1/√x+10
a. its domain is(-∞,0]and its range is(0,∞)
b. its domain is(-10,∞) and its range is(0,∞)
c. its domain is(-10, ∞)and its range is(-∞,∞)d. its domain is[-10,∞) and its range is
(-∞,0) u (0,∞)

we have

we know that

the denominator can not be equal to zero and the term inside the square root can't be negative.

so

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

D x>-3

Step-by-step explanation:

3(-x+2) < 15

-3x + 6< 15 (Subtract 6 from both sides)

-3x < 9 (Divide 3 on both sides)

x>-3 (Flip the inequality because the variable was negative)