Add and subtract functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

How do you add two functions?

Back

To add two functions f(x) and g(x), you combine them as (f + g)(x) = f(x) + g(x).

Front

What is the result of adding f(x) = 2x + 3 and g(x) = x - 5?

Back

(f + g)(x) = (2x + 3) + (x - 5) = 3x - 2.

Front

How do you subtract one function from another?

Back

To subtract two functions f(x) and g(x), you combine them as (f - g)(x) = f(x) - g(x).

Front

What is the result of subtracting g(x) = x - 5 from f(x) = 2x + 3?

Back

(f - g)(x) = (2x + 3) - (x - 5) = x + 8.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (f(x)) that the function can produce.

Front

What does it mean for two functions to be equal?

Back

Two functions f(x) and g(x) are equal if they produce the same output for every input in their domain.

Front

What is a composite function?

Back

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

Front

How do you find the composite of f(x) = 2x and g(x) = x + 1?

Back

(f ∘ g)(x) = f(g(x)) = f(x + 1) = 2(x + 1) = 2x + 2.