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 evaluate a composite function?

Back

To evaluate a composite function, first evaluate the inner function and then substitute that result into the outer function.

Front

Given f(x) = x^2 and g(x) = 3x - 1, find f(g(2)).

Back

f(g(2)) = f(5) = 25.

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) = 2x + 3 and g(x) = x^2, find g(f(1)).

Back

g(f(1)) = g(5) = 25.

Front

What is the domain of a composite function?

Back

The domain of a composite function is the set of all x values for which g(x) is in the domain of f.

Front

If f(x) = x - 1 and g(x) = 4x, find f(g(3)).

Back

f(g(3)) = f(12) = 11.

Front

What is the range of a composite function?

Back

The range of a composite function is the set of all possible output values of f(g(x)).

Front

Given f(x) = x^2 + 1 and g(x) = x - 2, find (f ∘ g)(3).

Back

(f ∘ g)(3) = f(1) = 2.

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.