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?

Back

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

Front

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

Back

The order of operations is INSIDE then OUT.

Front

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

Back

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

Front

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

Back

g(f(x)) = g(x - 1) = 3(x - 1) = 3x - 3.

Front

What is the domain of the composition f(g(x))?

Back

The domain of 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)), what does h(x) represent?

Back

h(x) represents the output of the function f when the input is the output of the function g applied to x.

Front

What is the range of a function composition?

Back

The range of a function composition f(g(x)) is the set of all possible outputs of f(g(x)).

Front

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

Back

f(g(3)) = f(2*3) = f(6) = 6 + 2 = 8.

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 can yield different results.