Function Operations and Composite Functions

Front

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

Back

The sum of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

How do you find the difference of two functions f(x) and g(x)?

Back

The difference of two functions f(x) and g(x) is defined as (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

Front

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

Back

The product of two functions f(x) and g(x) is defined as (f ⋅ g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

f(g(x)) = 2(x^2 + 3) = 2x^2 + 6.

Tags

CCSS.HSF-BF.A.1C

Front

If f(x) = x^2 + 9 and g(x) = x - 9, what is f(g(x))?

Back

f(g(x)) = f(x - 9) = (x - 9)^2 + 9 = x^2 - 18x + 81 + 9 = x^2 - 18x + 90.

Tags

CCSS.HSF-BF.A.1C

Front

What is the formula for finding f(g(x)) when f(x) = -3x + 7 and g(x) = 2x^2 - 8?

Back

f(g(x)) = -3(2x^2 - 8) + 7 = -6x^2 + 24 + 7 = -6x^2 + 31.

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate f(x) + g(x) for f(x) = 9 - 3x and g(x) = 5x - 7?

Back

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

Tags

CCSS.HSF-BF.A.1B

Front

What is the result of f(x) - g(x) for 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 + 4 and g(x) = 3x^2 - 1, what is f(x) ⋅ g(x)?

Back

f(x) ⋅ g(x) = (2x + 4)(3x^2 - 1) = 6x^3 + 12x^2 - 2x - 4.

Tags

CCSS.HSF-BF.A.1B