Solve the Problem $$f ( x ) = \sqrt { x + 3 }$$

question 144

Multiple Choice

Solve the problem.
- $$f ( x ) = \sqrt { x + 3 }$$
a. Graph $f ( x )$
b. Write an equation for $f ^ { - 1 } ( x )$
c. Write the domain of $f ^ { - 1 }$ in interval notation

• A) a. b. \(f ^ { - 1 } ( x ) = x ^ { 2 } - 3 ; x \geq - 3\); c. \([ - 3 , \infty )\)
• B) a. b. \(f ^ { - 1 } ( x ) = x ^ { 2 } + 3 ; x \geq 0\); c. \([ 0 , \infty )\)
• C) a. b. \(f ^ { - 1 } ( x ) = x ^ { 2 } + 3 ; x \geq 3\); c. \([ 3 , \infty )\)
• D) \(\mathbf { a }\). b. \(f ^ { - 1 } ( x ) = x ^ { 2 } - 3 ; x \geq 0\); c. \([ 0 , \infty )\)

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Definitions:

Complement

In probability theory, the event consisting of all outcomes not in a given event, typically leading to a sum of probabilities equal to one.

Probability

The quantification of an event's likelihood to occur, represented as a number from 0 to 1.

Mutually Exclusive Events

Two events that cannot occur at the same time within the same experiment or observation.

Independent Events

Two or more events that have no influence on each other's occurrence, meaning the occurrence of one event does not affect the probability of the other.