Composite Functions & Operations

Front

Define Composite Function.

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f∘g)(x) = f(g(x)).

Front

What is the formula for adding two functions f(x) and g(x)?

Back

The formula for adding two functions is (f + g)(x) = f(x) + g(x).

Front

What is the formula for subtracting two functions f(x) and g(x)?

Back

The formula for subtracting two functions is (f - g)(x) = f(x) - g(x).

Front

What is the formula for multiplying two functions f(x) and g(x)?

Back

The formula for multiplying two functions is (f * g)(x) = f(x) * g(x).

Front

What is the formula for composing two functions f(x) and g(x)?

Back

The formula for composing two functions is (f∘g)(x) = f(g(x)).

Front

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

Back

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

Front

Given f(x) = x - 1 and g(x) = 4x, find (f - g)(x).

Back

(f - g)(x) = (x - 1) - (4x) = -3x - 1.

Front

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

Back

g(2) = 3(2) + 1 = 7; f(g(2)) = f(7) = 7^2 = 49.

Front

What is the output of (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

(f∘g)(0) = f(g(0)) = f(-2) = 3(-2) + 10 = 4.

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) = x^2 + 8x + 1.