operation of functions

Front

Define the operation of functions.

Back

The operation of functions refers to the ways in which two or more functions can be combined to create new functions, including addition, subtraction, multiplication, and division.

Front

What is the sum of two functions f(n) and g(n)?

Back

The sum of two functions f(n) and g(n) is defined as (f + g)(n) = f(n) + g(n).

Front

If f(n) = 2n + 1 and g(n) = 3n, what is (f + g)(n)?

Back

(f + g)(n) = 5n + 1.

Front

What is the difference of two functions f(n) and g(n)?

Back

The difference of two functions f(n) and g(n) is defined as (f - g)(n) = f(n) - g(n).

Front

If f(n) = x^2 + 1 and g(n) = 2x - 5, what is (f - g)(n)?

Back

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

Front

Define the product of two functions f(x) and g(x).

Back

The product of two functions f(x) and g(x) is defined as (f * g)(x) = f(x) * g(x).

Front

If f(x) = 2x + 4 and g(x) = 3x^2 - 1, what is (f * g)(x)?

Back

(f * g)(x) = 6x^3 + 12x^2 - 2x - 4.

Front

What is the composition of functions f(g(x))?

Back

The composition of functions f(g(x)) is the application of function g to x, followed by the application of function f to the result.

Front

If f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, what is (f + g)(x)?

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

What is the formula for finding the difference of two quadratic functions?

Back

For f(x) = ax^2 + bx + c and g(x) = dx^2 + ex + f, the difference is (f - g)(x) = (a - d)x^2 + (b - e)x + (c - f).