Step 1, Step 2, and Step 3.
To solve sum of functions, you may need to take several steps to take to achieve the solution.
Since we’ve been learning functions so far, this time is also about a form of function, known as the sum of functions.
Description:
The sum of functions is a mathematical operation that involves adding together the values of two or more functions at each point in their domain. If you have two functions f(x) and g(x), their sum, denoted as (f+g)(x), is a new function that takes in a value of x, evaluates f(x) and g(x) separately, and then adds the results.
In other words, for any given value of x, the value of the sum function (f+g)(x) is equal to the sum of f(x) and g(x) evaluated at that same value of x. Mathematically, we can express this as:
(f+g)(x) = f(x) + g(x)
For example, if we have two simple functions f(x) = 2x and g(x) = x^2, their sum (f+g)(x) would be:
(f+g)(x) = f(x) + g(x) = 2x + x^2
The sum of functions is a fundamental operation in calculus, and it is used to manipulate and analyze mathematical models in many areas of science, engineering, and economics. It is also used to solve equations, optimize systems, and model real-world phenomena.
Actual handwriting samples:
From here, as always, let’s take a look at my handwriting samples on my Galaxy Tab S8+.
Find (f + g)(3)
f(x) = x^2 – x + 4.
g(x) = x – 2.
Solve f(x) = x^2 – x + 4 and substitute 3 in x.
Then, solve for g(x) = x – 2 and substitute 3 in x.
Then, suppose we get pairs of inputs and outputs for each function, instead of their equations, there’s only one way to add them, and that’s to add the corresponding outputs.
From here, let’s do some other samples:
Sample 1:
Sample 2:
