Question content area top
Part 1
Find a.​ (f plus g​)(x​) b.​ (f plus g​)(7​).
f​(x​)equals 3 x plus 4​, g​(x​)equals 5 x minus 1 
Question content area bottom
Part 1
a.  ​(f plus g​)(x​)equals
  
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To solve the problem, let's break it down step by step:

### Part a: Find \((f + g)(x)\)

The functions given are:

\[
f(x) = 3x + 4
\]
\[
g(x) = 5x - 1
\]

To find \((f + g)(x)\), we simply add the two functions:

\[
(f + g)(x) = f(x) + g(x)
\]

Substitute the given functions:

\[
(f + g)(x) = (3x + 4) + (5x - 1)
\]

Now combine like terms:

\[
(f + g)(x) = 3x + 5x + 4 - 1
\]
\[
(f + g)(x) = 8x + 3
\]

### Part b: Find \((f + g)(7)\)

Now substitute \(x = 7\) into the expression we found in part a:

\[
(f + g)(7) = 8(7) + 3
\]
\[
(f + g)(7) = 56 + 3 = 59
\]

### Final answers:
a. \((f + g)(x) = 8x + 3\)  
b. \((f + g)(7) = 59\)

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:
1. How would you find \((f - g)(x)\)?
2. What is \((f \cdot g)(x)\) for the same functions \(f(x)\) and \(g(x)\)?
3. How would you solve \((f/g)(x)\) for \(x = 2\)?
4. Can you graph the functions \(f(x)\) and \(g(x)\) on the same coordinate plane?
5. How would the solution change if \(g(x)\) was a quadratic function?

**Tip**: When combining functions, always remember to distribute and combine like terms carefully to avoid mistakes!

Part 1: Find (f + g)(x) and (f + g)(7). f(x) = 3x + 4, g(x) = 5x - 1.

Learn how to add linear functions f(x) = 3x + 4 and g(x) = 5x - 1, and solve for (f + g)(x) and (f + g)(7). This problem explains key algebra concepts and function operations, ideal for Grades 7-9.

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