Composition of Functions

Front

What is a function composition?

Back

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

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is (g∘h)(x)?

Back

(g∘h)(x) = 9x + 1.

Front

How do you find g(-2) if g(x) = 3x + 4?

Back

g(-2) = 3(-2) + 4 = -6 + 4 = -2.

Front

What is the result of p(q(x)) if p(x) = 3x + 4 and q(x) = 2x²?

Back

p(q(x)) = 6x² + 4.

Front

How do you evaluate f(-1) if f(x) = 2x² + 5x - 17?

Back

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

Front

What is the value of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

f(g(5)) = f(3) = 3(3) + 10 = 19.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if they produce the same output for every input in their domain.

Front

What is the notation for function composition?

Back

Function composition is denoted as (f∘g)(x), which means f(g(x)).