Composition of Functions

Front

What is the definition of composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

f(1) = 2(1) + 1 = 3.

Front

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

Back

g(5) = 5 - 3 = 2.

Front

What does it mean for a function to be undefined?

Back

A function is undefined when there is no valid output for a given input, often due to division by zero or taking the square root of a negative number.

Front

If f(g(3)) = 2 and g(3) = 1, what is f(1)?

Back

f(1) = 2.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f ∘ g)(x) or f(g(x)).

Front

If h(x) = x^2, what is h(-4)?

Back

h(-4) = (-4)^2 = 16.

Front

What is the value of g(h(-4)) if g(x) = x - 4?

Back

g(h(-4)) = g(16) = 16 - 4 = 12.

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(6) = 6 + 2 = 8.

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.