Question

If f(x) = 3x-2 and g(x) = x +1, find (f+g)(x).

Answer 1

`\huge\boxed{\sf (f+g)(x) = 4x - 1}`

Explanation:

Given functions:

• f(x) = 3x - 2
• g(x) = x + 1

Solution:

Add both functions

(f+g)(x) = 3x - 2 + x + 1

Combine like terms

(f+g)(x) = 3x + x - 2 + 1

(f+g)(x) = 4x - 1

`\rule[225]{225}{2}`

Answer 2

`(f+g)(x)=4x-1`

Explanation:

Functions

Functions written in equation form usually have several parts:

1. name
2. input
3. Mathematical rule/expression that tells what the function does to the input to give an output.

So, for instance,
`g(x)=x+1` has a name of "g", has an input of "x", and has a rule that it adds 1 to the input to get the output.

The name of the function should tell what rule to follow (look for the equation with that function name), or it may give some details on what the function does.

Dealing with so many different problems, functions often get a default name of "f", "g", or "h".

If a function is special and/or used commonly, it will sometimes get a special name (like the natural logarithm function "ln").

This function

In this case, the function is (f+g)(x). The function name means that the result of each function, f and g, will be added together, while using the same input "x" for both functions.

`(f+g)(x)=f(x)+g(x)\\=(3x-2)+(x+1)\\=3x+(-2)+x+1\\=4x+(-1)\\=4x-1`

So, given these two functions for "f" and "g",
`(f+g)(x)=4x-1`