Composition of Functions

Front

What is the definition of function composition?

Back

Function composition is the process of applying one function to the results of another function. If f and g are two functions, the composition of f and g is denoted as f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

If p(x) = 3x + 4 and q(x) = 2x^2, what is p(q(x))?

Back

p(q(x)) = 6x^2 + 4.

Tags

CCSS.HSF-BF.A.1C

Front

What is the result of f(g(x)) if f(x) = 5x and g(x) = 2x - 1?

Back

f(g(x)) = 10x - 5.

Tags

CCSS.HSF-BF.A.1C

Front

How do you evaluate g(-2) if g(x) = 2x^2 - 4?

Back

g(-2) = 2(-2)^2 - 4 = 8 - 4 = 4.

Tags

CCSS.HSF.IF.A.2

Front

What is the value of f(-1) if f(x) = 2x^2 + 5x - 17?

Back

f(-1) = 2(-1)^2 + 5(-1) - 17 = 2 - 5 - 17 = -20.

Tags

CCSS.HSF.IF.A.2

Front

If f(x) = 3x + 10 and g(x) = x - 2, what is f(g(5))?

Back

g(5) = 5 - 2 = 3, then f(g(5)) = f(3) = 3(3) + 10 = 19.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

The general formula for composing two functions is f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters; f(g(x)) is generally not the same as g(f(x)).

Tags

CCSS.HSF-BF.A.1C

Front

How do you find the composition of functions step by step?

Back

To find the composition of functions, substitute the input of the inner function into the outer function.

Tags

CCSS.HSF-BF.A.1C