Combine Functions using arithmetic

Front

Define the concept of combining functions using addition.

Back

Combining functions using addition involves creating a new function by adding the outputs of two functions for the same input. If f(n) and g(n) are two functions, then (f + g)(n) = f(n) + g(n).

Front

What is the formula for combining functions using subtraction?

Back

The formula for combining functions using subtraction is (f - g)(n) = f(n) - g(n). This means you subtract the output of g from the output of f for the same input n.

Front

How do you combine functions using multiplication?

Back

To combine functions using multiplication, you multiply the outputs of the two functions. If f(x) and g(x) are two functions, then (f ⋅ g)(x) = f(x) * g(x).

Front

What is the process for dividing two functions?

Back

Dividing two functions involves creating a new function by dividing the output of one function by the output of another. If f(x) and g(x) are two functions, then (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

Given f(n) = -n^2 - 4n and g(n) = 4n + 2, find (g + f)(n).

Back

(g + f)(n) = g(n) + f(n) = (4n + 2) + (-n^2 - 4n) = -n^2 + 2.

Front

If f(a) = a^3 - a and g(a) = 2a - 5, what is g(a) - f(a)?

Back

g(a) - f(a) = (2a - 5) - (a^3 - a) = -a^3 + 3a - 5.

Front

How do you simplify the expression (g/f)(x) where f(x) = 5x - 1 and g(x) = x - 7?

Back

(g/f)(x) = g(x) / f(x) = (x - 7) / (5x - 1).

Front

Calculate f(x) ⋅ g(x) for f(x) = 4x - 1 and g(x) = 2x + 2.

Back

f(x) ⋅ g(x) = (4x - 1)(2x + 2) = 8x^2 + 6x - 2.

Front

What is the result of (f ⋅ g)(x) if f(x) = x - 3 and g(x) = x + 4?

Back

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

Front

Define the term 'function composition'.

Back

Function composition is the process of applying one function to the result of another function. If f and g are functions, then the composition is denoted as (f ∘ g)(x) = f(g(x)).