Composite Functions

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), you first evaluate g(x) and then substitute that result into f(x).

Front

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

Back

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

Front

What is the value of (f∘g)(0) if f(x) = 3x + 10 and g(x) = x - 2?

Back

(f∘g)(0) = f(g(0)) = f(-2) = 3(-2) + 10 = 4.

Front

If h(a) = 3 - 2a, what is h(-3)?

Back

h(-3) = 3 - 2(-3) = 3 + 6 = 9.

Front

Which expression represents (f∘g)(x)?

Back

(f∘g)(x) is represented as f(g(x)).

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 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.

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 a composite function at a specific point?

Back

To evaluate a composite function at a specific point, first find the value of g at that point, then substitute that value into f.