Addition of Functions

Front

Define the addition of functions.

Back

The addition of functions is the operation of combining two functions, f(x) and g(x), to create a new function (f + g)(x) = f(x) + g(x).

Front

What is the formula for adding two linear functions f(x) = ax + b and g(x) = cx + d?

Back

(f + g)(x) = (a + c)x + (b + d).

Front

If f(x) = 2x + 3 and g(x) = 4x - 5, find (f + g)(x).

Back

(f + g)(x) = 6x - 2.

Front

What is the result of adding the functions f(x) = x^2 and g(x) = 3x + 1?

Back

(f + g)(x) = x^2 + 3x + 1.

Front

Given f(x) = 5 and g(x) = 2x, what is (f + g)(x)?

Back

(f + g)(x) = 2x + 5.

Front

If f(x) = x^2 - 4 and g(x) = 2x + 1, find (f + g)(x).

Back

(f + g)(x) = x^2 + 2x - 3.

Front

What is the addition of the functions f(n) = n^2 and g(n) = 3n - 2?

Back

(f + g)(n) = n^2 + 3n - 2.

Front

If f(x) = 3x^2 and g(x) = 2x^2 + x, what is (f + g)(x)?

Back

(f + g)(x) = 5x^2 + x.

Front

Define the term 'composite function'.

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the difference between the addition of functions and the composition of functions?

Back

Addition combines the outputs of two functions, while composition applies one function to the output of another.