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

Back

g(f(x)) = g(2x) = 2(2x)^2 - 1 = 8x^2 - 1.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

The product of two functions is given by (f ⋅ g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = 2x + 3 and g(x) = -3x - 4, what is f(x) * g(x)?

Back

f(x) * g(x) = (2x + 3)(-3x - 4) = -6x^2 - 17x - 12.

Tags

CCSS.HSF-BF.A.1B

Front

What is the value of f(g(3)) if f(x) = 2x and g(x) = 2x^2 - 1?

Back

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

Tags

CCSS.HSF-BF.A.1C

Front

What is the sum of two functions f(x) and g(x)?

Back

The sum of two functions is given by (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

If f(x) = 9 - 3x and g(x) = 5x - 7, what is f(x) + g(x)?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Tags

CCSS.HSF-BF.A.1B

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f(g(x)) or (f ∘ g)(x).

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = 1/x and g(x) = 3x + 2, what is (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)) applies g first and then f, while g(f(x)) applies f first and then g. They are generally not equal.

Tags

CCSS.HSF-BF.A.1C