composition of functions+function operations

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions, where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = 2x and g(x) = x + 3, what is (f ∘ g)(2)?

Back

(f ∘ g)(2) = f(g(2)) = f(2 + 3) = f(5) = 2(5) = 10.

Tags

CCSS.HSF-BF.A.1C

Front

Define the term 'function operation'.

Back

Function operations refer to the various ways functions can be combined or manipulated, including addition, subtraction, multiplication, division, and composition.

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

(f + g)(x) = f(x) + g(x) = (x + 1) + (2x) = 3x + 1.

Tags

CCSS.HSF-BF.A.1B

Front

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

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) = x + 1, what is (f ∘ g)(-1)?

Back

(f ∘ g)(-1) = f(g(-1)) = f(-1 + 1) = f(0) = 0^2 = 0.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) is the composition of f and g, where g is applied first, while g(f(x)) is the composition where f is applied first. They may yield different results.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = 1/x and g(x) = 3x + 2, find (f ∘ g)(2).

Back

(f ∘ g)(2) = f(g(2)) = f(3(2) + 2) = f(8) = 1/8.

Tags

CCSS.HSF-BF.A.1C

Front

What is the result of (g ∘ g)(-4) if g(x) = 3x + 2?

Back

(g ∘ g)(-4) = g(g(-4)) = g(3(-4) + 2) = g(-10) = 3(-10) + 2 = -28.

Tags

CCSS.HSF-BF.A.1C