If [tex]f(x)=-5^x-4[/tex] and [tex]g(x)=-3 x-2[/tex], find [tex](f+g)(x)[/tex]
A. [tex](f+g)(x)=-8 x-6[/tex]
B. [tex](f+g)(x)=5^x+3 x+6[/tex]
C. [tex](f+g)(x)=-5^x-7 x-2[/tex]
D. [tex](f+g)(x)=-5^x-3 x-6[/tex]

Add the two functions: ( f + g ) ( x ) = f ( x ) + g ( x ) .
Substitute the given expressions: ( f + g ) ( x ) = ( − 5 x − 4 ) + ( − 3 x − 2 ) .
Simplify the expression: ( f + g ) ( x ) = − 5 x − 3 x − 6 .
The final answer is: ( f + g ) ( x ) = − 5 x − 3 x − 6 ​ .

Explanation

Understanding the problem We are given two functions, f ( x ) = − 5 x − 4 and g ( x ) = − 3 x − 2 . Our goal is to find the sum of these two functions, which is denoted as ( f + g ) ( x ) .

Calculating the sum of the functions To find ( f + g ) ( x ) , we simply add the two functions together: ( f + g ) ( x ) = f ( x ) + g ( x ) Now, we substitute the expressions for f ( x ) and g ( x ) :
( f + g ) ( x ) = ( − 5 x − 4 ) + ( − 3 x − 2 ) Next, we simplify the expression by combining like terms: ( f + g ) ( x ) = − 5 x − 4 − 3 x − 2 ( f + g ) ( x ) = − 5 x − 3 x − 6

Finding the correct option The result is ( f + g ) ( x ) = − 5 x − 3 x − 6 . Comparing this to the given options, we see that it matches option D.


Examples
In economics, if f ( x ) represents the cost of production and g ( x ) represents the revenue, then ( f + g ) ( x ) could represent the overall profit or loss at a given production level x . Understanding how to combine these functions helps in analyzing the financial performance of a business.

Answered by GinnyAnswer | 2025-07-08