If [tex]f(x)=2x[/tex] and [tex]g(x)=5x+2[/tex], what is [tex](f+g)(x)[/tex] when [tex]x=3[/tex]?

Find the sum of the functions: ( f + g ) ( x ) = f ( x ) + g ( x ) = 2 x + ( 5 x + 2 ) .
Simplify the expression: ( f + g ) ( x ) = 7 x + 2 .
Substitute x = 3 into the expression: ( f + g ) ( 3 ) = 7 ( 3 ) + 2 .
Calculate the final value: ( f + g ) ( 3 ) = 23 , so the answer is 23 ​ .

Explanation

Understanding the problem We are given two functions, f ( x ) = 2 x and g ( x ) = 5 x + 2 . We want to find the value of ( f + g ) ( x ) when x = 3 . This means we first need to find the expression for ( f + g ) ( x ) , and then substitute x = 3 into that expression.

Adding the functions To find ( f + g ) ( x ) , we simply add the two functions together: ( f + g ) ( x ) = f ( x ) + g ( x ) Substituting the given expressions for f ( x ) and g ( x ) , we get: ( f + g ) ( x ) = 2 x + ( 5 x + 2 )

Simplifying the expression Now, we simplify the expression by combining like terms: ( f + g ) ( x ) = 2 x + 5 x + 2 = 7 x + 2

Substituting x=3 Next, we substitute x = 3 into the simplified expression for ( f + g ) ( x ) :
( f + g ) ( 3 ) = 7 ( 3 ) + 2

Calculating the final value Finally, we calculate the numerical value: ( f + g ) ( 3 ) = 21 + 2 = 23 So, ( f + g ) ( 3 ) = 23 .


Examples
In real life, combining functions like this can model scenarios where you have two different sources of income or expenses. For example, imagine you earn 2 x dollars from a part-time job and 5 x + 2 dollars from a side business, where x is the number of hours you work. The function ( f + g ) ( x ) = 7 x + 2 represents your total earnings. If you work 3 hours ( x = 3 ), your total earnings would be ( f + g ) ( 3 ) = 7 ( 3 ) + 2 = 23 dollars.

Answered by GinnyAnswer | 2025-07-05