Composite Functions Review

Front

What is a composite function?

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find f(g(x))?

Back

To find f(g(x)), first evaluate g(x) for a specific x value, then substitute that result into f(x).

Front

Given f(x) = 4x - 5 and g(x) = x^2 + 3, find f(g(2)).

Back

f(g(2)) = f(2^2 + 3) = f(7) = 4(7) - 5 = 28 - 5 = 23.

Front

Given f(x) = 3x + 10 and g(x) = x - 2, find f(g(5)).

Back

f(g(5)) = f(5 - 2) = f(3) = 3(3) + 10 = 9 + 10 = 19.

Front

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

Back

f(g(3)) = f(3^2 - 1) = f(8) = 3(8) + 2 = 24 + 2 = 26.

Front

What is the notation for composite functions?

Back

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

Front

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

Back

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

Front

If f(x) = 2x - 8 and g(x) = 4x, what is g(f(x))?

Back

g(f(x)) = g(2x - 8) = 4(2x - 8) = 8x - 32.

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 values for which g(x) is in the domain of f.

Front

How do you evaluate a composite function at a specific point?

Back

To evaluate a composite function at a specific point, first find the value of the inner function, then use that result to evaluate the outer function.