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which of the following is true about the function below? 1/√x+10

AIts domain is(-∞,0]and its range is(0,∞)
BIts domain is(-10,∞) and its range is(0,∞)
CIts domain is(-10, ∞)and its range is(-∞,∞)D. Its domain is[-10,∞) and its range is

(-∞,0) U (0,∞)



...?

Verified Answer :

calculista

we have

\(f(x)=\frac{1}{\sqrt{x+10}}\)

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

View image calculista

Answer:

B

Step-by-step explanation:

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