If [tex]$f(x)=5 x-2$[/tex] and [tex]$g(x)=2 x+1$[/tex], find [tex]$(f+g)(x)$[/tex]
A. [tex]$7 x-1$[/tex]
B. [tex]$3 x-1$[/tex]
C. [tex]$4 x-3$[/tex]
D. [tex]$7 x-3$[/tex]

Add the two functions: ( f + g ) ( x ) = f ( x ) + g ( x ) .
Substitute the given expressions: ( f + g ) ( x ) = ( 5 x − 2 ) + ( 2 x + 1 ) .
Combine like terms: ( f + g ) ( x ) = 5 x + 2 x − 2 + 1 .
Simplify the expression: ( f + g ) ( x ) = 7 x − 1 . The final answer is 7 x − 1 ​ .

Explanation

Understanding the problem We are given two functions, f ( x ) = 5 x − 2 and g ( x ) = 2 x + 1 . We want to find ( f + g ) ( x ) , which means we need to add the two functions together.

Adding the functions To find ( f + g ) ( x ) , we add the expressions for f ( x ) and g ( x ) :
( f + g ) ( x ) = f ( x ) + g ( x ) = ( 5 x − 2 ) + ( 2 x + 1 ) Now, we combine like terms.

Simplifying the expression We combine the x terms and the constant terms: ( f + g ) ( x ) = ( 5 x + 2 x ) + ( − 2 + 1 ) ( f + g ) ( x ) = 7 x − 1

Final Answer Therefore, ( f + g ) ( x ) = 7 x − 1 .


Examples
Understanding function addition is useful in many real-world scenarios. For example, if you have two different sources of income, say from a part-time job and a side business, you can represent each income stream as a function of time. Adding these functions together gives you your total income as a function of time. This helps in budgeting and financial planning.

Answered by GinnyAnswer | 2025-07-03

The sum of the functions f ( x ) = 5 x − 2 and g ( x ) = 2 x + 1 is ( f + g ) ( x ) = 7 x − 1 . Therefore, the correct answer is option A: 7 x − 1 .
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Answered by Anonymous | 2025-07-04