If [tex]$f(x)=3^x+10$[/tex] and [tex]$g(x)=2 x-4$[/tex], find [tex]$(f-g)(x)$[/tex]
A. [tex]$(f-g)(x)=3^x+2 x+6$[/tex]
B. [tex]$(f-g)(x)=3^x-2 x+14$[/tex]
C. [tex]$(f-g)(x)=-3^x+2 x-14$[/tex]
D. [tex]$(f-g)(x)=x+14$[/tex]

To find ( f − g ) ( x ) , we calculated f ( x ) − g ( x ) , which led us to the result: 3 x − 2 x + 14 . This corresponds to option B.
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Answered by Anonymous | 2025-07-08

Recognize that ( f − g ) ( x ) = f ( x ) − g ( x ) .
Substitute the given functions: ( f − g ) ( x ) = ( 3 x + 10 ) − ( 2 x − 4 ) .
Distribute the negative sign: ( f − g ) ( x ) = 3 x + 10 − 2 x + 4 .
Combine like terms to get the final expression: ( f − g ) ( x ) = 3 x − 2 x + 14 ​ .

Explanation

Understanding the problem We are given two functions, f ( x ) = 3 x + 10 and g ( x ) = 2 x − 4 . Our goal is to find the expression for ( f − g ) ( x ) .

Defining the operation Recall that ( f − g ) ( x ) means f ( x ) − g ( x ) . So, we need to subtract the function g ( x ) from the function f ( x ) .

Substituting the functions Substitute the given expressions for f ( x ) and g ( x ) into the equation: ( f − g ) ( x ) = ( 3 x + 10 ) − ( 2 x − 4 )

Distributing the negative sign Now, simplify the expression by distributing the negative sign and combining like terms: ( f − g ) ( x ) = 3 x + 10 − 2 x + 4

Combining like terms Combine the constant terms: ( f − g ) ( x ) = 3 x − 2 x + 14

Final Answer The expression for ( f − g ) ( x ) is 3 x − 2 x + 14 . Comparing this with the given options, we see that it matches option B.


Examples
In economics, let's say f ( x ) represents the total revenue of a company based on the quantity of items sold ( x ), and g ( x ) represents the total cost. Then, ( f − g ) ( x ) would represent the profit of the company. Understanding how to combine and simplify these functions helps in analyzing the financial performance of the company.

Answered by GinnyAnswer | 2025-07-08