Question

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,∞)


...?

Answer 1

B

Explanation:

Answer 2

we have

`f(x)=(1)/(√(x+10))`

we know that

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

so

`(x+10) > 0\\x > -10`

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