Composition of Functions Weekly HW

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. It is denoted as (f o g)(x) = f(g(x)).

Front

How do you evaluate h(g(2)) if h(x) = -4x + 3 and g(x) = 2x + 3?

Back

First, evaluate g(2): g(2) = 2(2) + 3 = 7. Then, evaluate h(7): h(7) = -4(7) + 3 = -28 + 3 = -25.

Front

What is the value of f(g(2)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

First, evaluate g(2): g(2) = 2(2) + 3 = 7. Then, evaluate f(7): f(7) = 3(7) + 6 = 21 + 6 = 27.

Front

How do you find f(g(-1)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

First, evaluate g(-1): g(-1) = 2(-1) + 3 = 1. Then, evaluate f(1): f(1) = 3(1) + 6 = 3 + 6 = 9.

Front

What is the formula for f(g(x)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

f(g(x)) = f(2x + 3) = 3(2x + 3) + 6 = 6x + 9 + 6 = 6x + 15.

Front

What does f o g(-3) represent?

Back

f o g(-3) represents the composition of functions f and g evaluated at -3, which means first applying g to -3 and then applying f to the result.

Front

How do you evaluate h o f(0) if h(x) = -4x + 3 and f(x) = x - 4?

Back

First, evaluate f(0): f(0) = 0 - 4 = -4. Then, evaluate h(-4): h(-4) = -4(-4) + 3 = 16 + 3 = 19.

Front

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

Back

The order of functions in composition matters because (f o g)(x) is not necessarily equal to (g o f)(x). The output of g becomes the input of f.

Front

What is the domain of the composition of functions?

Back

The domain of the composition f o g is the set of all x in the domain of g such that g(x) is in the domain of f.

Front

How do you find the range of a composition of functions?

Back

The range of the composition f o g is determined by the range of g and how it maps into the domain of f.