Function Composition and Evaluation

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f and g are two functions, the composition of f and g is denoted as (f ° g)(x) = f(g(x)).

Front

How do you evaluate a composite function?

Back

To evaluate a composite function (f ° g)(x), first evaluate g(x), then take that result and substitute it into f.

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

Back

(f ° g)(2) = f(g(2)) = f(2 + 3) = f(5) = 2(5) = 10.

Front

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

Back

g(f(-1)) = g(2(-1)) = g(-2) = (-2)^2 - 1 = 4 - 1 = 3.

Front

What does it mean if a composite function is undefined?

Back

A composite function is undefined if the inner function's output is not in the domain of the outer function.

Front

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

Back

(g ° f)(1) = g(f(1)) = g(1^2) = g(1) = 3(1) + 1 = 4.

Front

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

Back

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

Front

If f(x) = 4x - 1 and g(x) = x^2, what is f(g(1))?

Back

f(g(1)) = f(1^2) = f(1) = 4(1) - 1 = 3.

Front

What is the output of (f ° g)(-1) if f(x) = x + 5 and g(x) = 2x?

Back

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