Composite Functions

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Front

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

Back

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

Front

What is the notation for composite functions?

Back

The notation for composite functions is (f∘g)(x), which means f(g(x)).

Front

If f(x) = x^2 and g(x) = 3x - 1, what is f(g(x))?

Back

f(g(x)) = f(3x - 1) = (3x - 1)^2 = 9x^2 - 6x + 1.

Front

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

Back

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

Front

What is the domain of a composite function?

Back

The domain of a composite function f(g(x)) 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 evaluate (f∘g)(3) if f(x) = √(4x - 4) and g(x) = 3x + 1?

Back

(f∘g)(3) = f(g(3)) = f(3(3) + 1) = f(10) = √(4(10) - 4) = √(36) = 6.

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.

Front

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

Back

f(g(2)) = f(2^2 + 3) = f(7) = 2(7) = 14.

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.