$\begin{array}{l}
f(x)=2 x-1 \\
g(x)=7 x-12
\end{array}$
What is $h(x)=f(x)+g(x) ?$
A. $h(x)=9 x-13$
B. $h(x)=9 x-12$
C. $h(x)=-5 x+11$
D. $h(x)=5 x-13
Answer (1)
Add the expressions for f ( x ) and g ( x ) : h ( x ) = ( 2 x − 1 ) + ( 7 x − 12 ) .
Combine like terms: h ( x ) = ( 2 x + 7 x ) + ( − 1 − 12 ) .
Simplify the expression: h ( x ) = 9 x − 13 .
The correct expression for h ( x ) is 9 x − 13 .
Explanation
Understanding the problem We are given two functions, f ( x ) = 2 x − 1 and g ( x ) = 7 x − 12 . We need to find the function h ( x ) which is the sum of f ( x ) and g ( x ) . In other words, we need to find h ( x ) = f ( x ) + g ( x ) .
Adding the functions To find h ( x ) , we add the expressions for f ( x ) and g ( x ) :
h ( x ) = f ( x ) + g ( x ) = ( 2 x − 1 ) + ( 7 x − 12 ) Now, we combine like terms. We add the terms with x and the constant terms: h ( x ) = ( 2 x + 7 x ) + ( − 1 − 12 ) h ( x ) = 9 x − 13
Comparing with the choices Now we compare our result, h ( x ) = 9 x − 13 , with the given choices:
h ( x ) = 9 x − 13
h ( x ) = 9 x − 12
h ( x ) = − 5 x + 11
h ( x ) = 5 x − 13
The first choice, h ( x ) = 9 x − 13 , matches our result.
Final Answer Therefore, the correct expression for h ( x ) is 9 x − 13 .
Examples
Imagine you're tracking your expenses and income. Let's say f ( x ) represents your daily expenses, where x is the number of days, and g ( x ) represents your daily income. Finding h ( x ) = f ( x ) + g ( x ) would give you a combined function representing your overall financial situation each day. This helps you quickly see whether you're making a profit or running a deficit over time. Understanding how to combine these functions allows for easy financial tracking and planning.
