$f(x)=x^2+1 \quad g(x)=5-x$

$(f+g)(x)=$

A. $x^2+x-4$
B. $x^2+x+4$
C. $x^2-x+6$
D. $x^2+x+6$

We found that ( f + g ) ( x ) = x 2 − x + 6 by adding the functions f ( x ) = x 2 + 1 and g ( x ) = 5 − x . The correct answer is option C: x 2 − x + 6 .
;

Answered by Anonymous | 2025-07-08

Add the two functions: ( f + g ) ( x ) = f ( x ) + g ( x ) .
Substitute the expressions: ( f + g ) ( x ) = ( x 2 + 1 ) + ( 5 − x ) .
Simplify the expression: ( f + g ) ( x ) = x 2 − x + 6 .
The sum of the functions is x 2 − x + 6 ​ .

Explanation

Understanding the problem We are given two functions, f ( x ) = x 2 + 1 and g ( x ) = 5 − x . We need to find the sum of these two functions, which is denoted as ( f + g ) ( x ) .

Adding 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 given expressions for f ( x ) and g ( x ) :
( f + g ) ( x ) = ( x 2 + 1 ) + ( 5 − x ) Next, we simplify the expression by combining like terms:

Simplifying the expression ( f + g ) ( x ) = x 2 − x + 1 + 5 ( f + g ) ( x ) = x 2 − x + 6

Finding the correct option Therefore, ( f + g ) ( x ) = x 2 − x + 6 . Comparing this with the given options, we see that the correct answer is x 2 − x + 6 .


Examples
Understanding how to combine functions is essential in many real-world applications. For example, if you have a cost function f ( x ) representing the cost of producing x items and a revenue function g ( x ) representing the revenue from selling x items, then the profit function ( f + g ) ( x ) (or more accurately, g ( x ) − f ( x ) ) represents the total profit you make from producing and selling x items. By understanding how to combine these functions, you can analyze and optimize your business decisions.

Answered by GinnyAnswer | 2025-07-08