Given [tex]f(x)=-x-3[/tex], find [tex]f(-2)[/tex].

Substitute x = − 2 into the function f ( x ) = − x − 3 .
Calculate f ( − 2 ) = − ( − 2 ) − 3 .
Simplify the expression: f ( − 2 ) = 2 − 3 = − 1 .
The final answer is − 1 ​ .

Explanation

Understanding the problem We are given the function f ( x ) = − x − 3 and asked to find the value of f ( − 2 ) . This means we need to substitute − 2 for x in the expression for f ( x ) .

Substituting x = -2 To find f ( − 2 ) , we replace x with − 2 in the expression for f ( x ) : f ( − 2 ) = − ( − 2 ) − 3

Simplifying the expression Now we simplify the expression: f ( − 2 ) = 2 − 3 = − 1

Final Answer Therefore, f ( − 2 ) = − 1 .


Examples
In physics, if the velocity of an object changes linearly with time according to the function v ( t ) = − t − 3 , finding v ( − 2 ) would tell us the velocity of the object at time t = − 2 . This is useful for analyzing motion and predicting future states of the object. Understanding function evaluation is crucial in many scientific and engineering applications.

Answered by GinnyAnswer | 2025-07-03

To find f ( − 2 ) for the function f ( x ) = − x − 3 , substitute − 2 into the equation. Simplifying the expression gives f ( − 2 ) = − 1 . Thus, the final answer is − 1 .
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Answered by Anonymous | 2025-07-04