2.12 Assign Composition of Functions PC

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f o g)(x), is the application of one function to the results of another function. It means that you first apply g to x, and then apply f to the result of g.

Front

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

Back

(f o g)(x) = f(g(x)) = f(x + 3) = 2(x + 3) = 2x + 6.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as f(x) = x.

Front

Can the identity function be used in function composition for (f o g)(x)?

Back

No, in this context, neither function f nor g can be the identity function.

Front

If h(x) = (f o g)(x) and h(x) = 3x + 5, what could be a possible form of f(x) and g(x)?

Back

One possible solution is f(x) = 3x and g(x) = x + 5.

Front

What is the notation for function composition?

Back

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

Front

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

Back

(f o g)(x) = f(g(x)) = f(2x) = (2x)^2 = 4x^2.

Front

What is the difference between (f o g)(x) and (g o f)(x)?

Back

(f o g)(x) applies g first and then f, while (g o f)(x) applies f first and then g. They are generally not equal.

Front

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

Back

(g o f)(x) = g(f(x)) = g(x + 1) = 3(x + 1) = 3x + 3.

Front

What is the domain of the composite function (f o g)(x)?

Back

The domain of (f o g)(x) is the set of all x in the domain of g such that g(x) is in the domain of f.