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For the given functions f and g, complete parts (a)-(h).

f(x) = 2x + 7
g(x) = 7x - 4

(a) Find (f + g)(x).

(f + g)(x) = __________ (Simplify your answer.)

Sagot :

GinnyAnswer
To find [tex]\((f+g)(x)\)[/tex] for the given functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex], follow these steps:

1. Identify the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ f(x) = 2x + 7 \][/tex]
[tex]\[ g(x) = 7x - 4 \][/tex]

2. Add the functions [tex]\( f \)[/tex] and [tex]\( g \)[/tex]:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]

3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f+g)(x) = (2x + 7) + (7x - 4) \][/tex]

4. Combine like terms:
[tex]\[ (f+g)(x) = 2x + 7x + 7 - 4 \][/tex]

5. Simplify the expression:
[tex]\[ (f+g)(x) = (2x + 7x) + (7 - 4) \][/tex]
[tex]\[ (f+g)(x) = 9x + 3 \][/tex]

So, the simplified form of [tex]\((f+g)(x)\)[/tex] is:
[tex]\[ (f+g)(x) = 9x + 3 \][/tex]
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