Function Notation & Composite Functions

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols. It typically uses the format f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function. It is denoted as (f∘g)(x) = f(g(x)).

Front

How do you find the range of a function?

Back

To find the range of a function, determine all possible output values (y-values) that the function can produce based on its domain.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Given f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

If f(x) = x^2 and g(x) = x + 1, what is g(f(2))?

Back

g(f(2)) = g(2^2) = g(4) = 4 + 1 = 5.

Front

What does f(g(x)) mean?

Back

f(g(x)) means to first apply the function g to x, and then apply the function f to the result of g(x).

Front

If f(x) = 3x - 5, what is f(0)?

Back

f(0) = 3(0) - 5 = -5.

Front

What is the output of f(g(1)) if f(x) = x^2 and g(x) = 2x + 1?

Back

f(g(1)) = f(2(1) + 1) = f(3) = 3^2 = 9.

Front

How do you evaluate (f∘g)(x)?

Back

To evaluate (f∘g)(x), substitute g(x) into f. This means you replace x in f with g(x).