Composition of Functions and Function Operations

Front

Define composition of functions.

Back

The composition of functions is an operation that takes two functions, f and g, and produces a new function, denoted as (f ∘ g)(x) = f(g(x)). It means applying function g first and then applying function f to the result.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

The formula for the composition of two functions is (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) = f(3x + 2) = (3x + 2)^2 = 9x^2 + 12x + 4.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) = f(2x^2 - 1) = 2(2x^2 - 1) = 4x^2 - 2.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate g(f(-1)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

First, find f(-1): f(-1) = 2(-1) = -2. Then, find g(-2): g(-2) = 2(-2)^2 - 1 = 8 - 1 = 7.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g. The order of operations matters.

Tags

CCSS.HSF-BF.A.1C

Front

Define function operations.

Back

Function operations include addition, subtraction, multiplication, and division of functions, allowing for the combination of functions to create new functions.

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = x + 1 and g(x) = x - 1, what is (f + g)(x)?

Back

(f + g)(x) = f(x) + g(x) = (x + 1) + (x - 1) = 2x.

Tags

CCSS.HSF-BF.A.1B