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Given the functions:

[tex]\[
\begin{array}{l}
f(x) = 2x - 1 \\
g(x) = 7x - 12
\end{array}
\][/tex]

What is [tex]\( h(x) = f(x) + g(x) \)[/tex]?

A. [tex]\( h(x) = 9x - 13 \)[/tex]

B. [tex]\( h(x) = 9x - 12 \)[/tex]

C. [tex]\( h(x) = -5x + 11 \)[/tex]

D. [tex]\( h(x) = 5x - 13 \)[/tex]



Answer :

GinnyAnswer
To find [tex]\( h(x) \)[/tex], we need to add the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex].

1. Let's start by expanding both [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ f(x) = 2x - 1 \][/tex]
[tex]\[ g(x) = 7x - 12 \][/tex]

2. Now, let's add [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] together to get [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = f(x) + g(x) \][/tex]
Substituting [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ h(x) = (2x - 1) + (7x - 12) \][/tex]
Combine the like terms:
[tex]\[ h(x) = 2x + 7x - 1 - 12 \][/tex]
[tex]\[ h(x) = 9x - 13 \][/tex]

So, the correct expression for [tex]\( h(x) \)[/tex] is:

[tex]\[ h(x) = 9x - 13 \][/tex]

Therefore, the correct answer is [tex]\( h(x) = 9x - 13 \)[/tex].

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