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 f(x) and g(x) are two functions, then the composition of f and g is denoted as (f ° g)(x) = f(g(x)).

Front

If f(x) = x - 5, what is f(2)?

Back

f(2) = 2 - 5 = -3.

Front

If g(x) = 3x^2 - 1, what is g(1)?

Back

g(1) = 3(1)^2 - 1 = 2.

Front

What is the notation for function composition?

Back

The notation for function composition is (f ° g)(x), which means f(g(x)).

Front

If f(x) = 3x - 1 and g(x) = x^2 + 2, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(x^2 + 2) = 3(x^2 + 2) - 1 = 3x^2 + 6 - 1 = 3x^2 + 5.

Front

What is the value of (f ° g)(-1) if f(x) = x - 5 and g(x) = 3x^2 - 1?

Back

(f ° g)(-1) = f(g(-1)) = f(3(-1)^2 - 1) = f(2) = 2 - 5 = -3.

Front

If h(x) = 3x - 1, what is h(0)?

Back

h(0) = 3(0) - 1 = -1.

Front

If g(x) = 3x + 4, what is g(2)?

Back

g(2) = 3(2) + 4 = 10.

Front

What is the result of g(h(x)) if g(x) = 3x + 4 and h(x) = 3x - 1?

Back

g(h(x)) = g(3x - 1) = 3(3x - 1) + 4 = 9x - 3 + 4 = 9x + 1.

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.