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. If you have two functions, f(x) and g(x), the composition is denoted as f(g(x)).

Front

How do you denote the composition of functions f and g?

Back

The composition of functions f and g is denoted as (f ∘ g)(x) or f(g(x)).

Front

What is the order of operations when evaluating f(g(x))?

Back

The order of operations is INSIDE then OUT, meaning you evaluate g(x) first, then apply f to that result.

Front

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

Back

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

Front

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

Back

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

Front

What is the domain of the composition of functions?

Back

The domain of the composition 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

If h(x) = f(g(x)), how do you find g(h(x))?

Back

To find g(h(x)), you substitute h(x) into g, which means you replace x in g with f(g(x)).

Front

What is the range of a function composition?

Back

The range of a composition f(g(x)) is determined by the range of g(x) and how it fits into the domain of f.

Front

If f(x) = rac{1}{x} and g(x) = x + 1, what is f(g(x))?

Back

f(g(x)) = f(x + 1) = rac{1}{x + 1}.

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, leading to potentially different results.