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 (g ∘ f)(x) = g(f(x)).

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) = x.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for function operations?

Back

Function operations include addition, subtraction, multiplication, and division of functions, defined as (f ± g)(x) = f(x) ± g(x), (f * g)(x) = f(x) * g(x), and (f / g)(x) = f(x) / g(x) for g(x) ≠ 0.

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

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

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 f(x) - g(x) if f(x) = x^2 + 9 and g(x) = x - 9?

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = 2x and g(x) = 2x^2 - 1, what is f(g(3))?

Back

g(3) = 2(3^2) - 1 = 17, then f(g(3)) = f(17) = 2(17) = 34.

Tags

CCSS.HSF-BF.A.1C

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if (f ∘ g)(x) = x and (g ∘ f)(x) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B