Function Operations & Compositions of Functions

Front

Define function operations.

Back

Function operations refer to the mathematical processes of combining two or more functions through addition, subtraction, multiplication, or division.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function, denoted as (f∘g)(x) = f(g(x)).

Front

Find (g∘h)(x) if g(x)=3x+4 and h(x)=3x-1.

Back

(g∘h)(x) = g(h(x)) = g(3x-1) = 3(3x-1) + 4 = 9x - 3 + 4 = 9x + 1.

Front

What is the formula for (f + g)(x)?

Back

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

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

Front

How do you evaluate f(g(0))?

Back

First, find g(0), then substitute that value into f(x).

Front

Evaluate f(-1) for f(x)=x^2-2x+1.

Back

f(-1) = (-1)^2 - 2(-1) + 1 = 1 + 2 + 1 = 4.

Front

What is the formula for (f⋅g)(x)?

Back

(f⋅g)(x) = f(x) * g(x).

Front

Given f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, find (f⋅g)(x).

Back

(f⋅g)(x) = (3x^2 - 2x + 1)(x - 4) = 3x^3 - 14x^2 + 9x - 4.

Front

What is the difference between (f - g)(x) and (f + g)(x)?

Back

(f - g)(x) = f(x) - g(x) and (f + g)(x) = f(x) + g(x).