Given [tex]f(x)=-x-2[/tex], find [tex]f(-6)[/tex].

Substitute x = − 6 into the function f ( x ) = − x − 2 .
Simplify the expression − ( − 6 ) − 2 .
Calculate 6 − 2 .
The final answer is 4 ​ .

Explanation

Understanding the problem We are given the function f ( x ) = − x − 2 and asked to find the value of f ( − 6 ) . This means we need to substitute − 6 for x in the expression for f ( x ) .

Substituting the value To find f ( − 6 ) , we substitute x = − 6 into the function: f ( − 6 ) = − ( − 6 ) − 2

Simplifying the expression Now we simplify the expression. The negative of − 6 is 6 , so we have: f ( − 6 ) = 6 − 2

Calculating the final value Finally, we subtract 2 from 6 to get the result: f ( − 6 ) = 4


Examples
In physics, if you have a formula that describes the position of an object at time t, such as f ( t ) = − t − 2 , you can find the position of the object at a specific time, say t = − 6 , by substituting − 6 into the formula. This gives you the object's position at that particular moment. Similarly, in economics, if f ( x ) represents the cost of producing x items, you can find the cost of producing a specific number of items by substituting that number into the function.

Answered by GinnyAnswer | 2025-07-03

To find f ( − 6 ) for the function f ( x ) = − x − 2 , we substitute − 6 into the function and simplify it to get 4 . The calculation shows that f ( − 6 ) = 4 after evaluating the function. Thus, the final answer is 4 .
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Answered by Anonymous | 2025-07-04