2.3-Composition Of Functions

Front

Define composition of functions.

Back

The composition of functions is an operation that takes two functions, f and g, and produces a new function, denoted as (f ∘ g)(x) = f(g(x)). It means applying the function g first and then applying the function f to the result.

Front

What is the notation for the composition of functions f and g?

Back

The notation for the composition of functions f and g is f ∘ g.

Front

If f(x) = x^2 and g(x) = x + 1, find (f ∘ g)(2).

Back

(f ∘ g)(2) = f(g(2)) = f(3) = 3^2 = 9.

Front

What is the domain of the composition of functions?

Back

The domain of the composition f ∘ g 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) = 2x and g(x) = x - 3, find g(f(5)).

Back

g(f(5)) = g(10) = 10 - 3 = 7.

Front

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

Back

(g ∘ f)(1) = g(f(1)) = g(0) = 3(0) + 4 = 4.

Front

What is the result of (f ∘ g)(x) if f(x) = x + 2 and g(x) = 2x?

Back

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

Front

If h(x) = -x and f(x) = x^2, find (f ∘ h)(-3).

Back

(f ∘ h)(-3) = f(h(-3)) = f(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 unless f and g have specific properties.

Front

If f(x) = x^2 - 2 and g(x) = x + 9, find f(g(-2)).

Back

f(g(-2)) = f(7) = 7^2 - 2 = 49 - 2 = 47.