Function Composition

Front

What is 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, the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

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

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

Back

g(f(2)) = g(2^2) = g(4) = 3(4) = 12.

Front

What is the domain of the composition (f ∘ g)(x)?

Back

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

Front

If f(x) = x + 5 and g(x) = 2x, what is (f ∘ g)(3)?

Back

(f ∘ g)(3) = f(g(3)) = f(2(3)) = f(6) = 6 + 5 = 11.

Front

What is the range of the composition (f ∘ g)(x)?

Back

The range of (f ∘ g)(x) is the set of all possible output values of f(g(x)).

Front

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

Back

(g ∘ f)(1) = g(f(1)) = g(1 - 4) = g(-3) = (-3)^2 = 9.

Front

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

Back

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

Front

If f(x) = 5x and g(x) = x/2, what is (f ∘ g)(4)?

Back

(f ∘ g)(4) = f(g(4)) = f(4/2) = f(2) = 5(2) = 10.