Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a way to combine two functions where the output of one function becomes the input of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

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

Back

(f ∘ g)(x) = f(g(x)) = f(x^2) = 2(x^2) + 3 = 2x^2 + 3.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f ∘ g, which means 'f composed with g'.

Front

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

Back

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

Front

What is the domain of the composition of functions?

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

Back

(f ∘ g)(x) = f(g(x)) = f(x - 1) = (x - 1)^2 = x^2 - 2x + 1.

Front

What is the range of the function f(x) = x^2?

Back

The range of f(x) = x^2 is [0, ∞) since the output is always non-negative.

Front

If f(x) = 3x - 2 and g(x) = 4x + 1, find (f ∘ g)(x).

Back

(f ∘ g)(x) = f(g(x)) = f(4x + 1) = 3(4x + 1) - 2 = 12x + 3 - 2 = 12x + 1.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

The inverse function f^(-1)(x) = (x - 3)/2.

Front

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

Back

f(2) = 2^2 + 1 = 4 + 1 = 5.