Day 66 Alg 2 Composition of Functions

Front

What is a function composition?

Back

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

Front

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

Back

(g ∘ f)(x) = g(f(x)) = g(2x + 3) = (2x + 3)^2 = 4x^2 + 12x + 9.

Front

What is the notation for function composition?

Back

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

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(3(2) + 1) = f(7) = 7^2 = 49.

Front

What is the domain of a composite function?

Back

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

Front

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

Back

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

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

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

Back

(f ∘ g)(x) = f(g(x)) = f(x^2) = x^2 + 4.

Front

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

Back

f(g(x)) applies g first and then f to the result, while g(f(x)) applies f first and then g to the result. They may yield different outputs.

Front

If f(x) = 3x - 5 and g(x) = x/2, find (f ∘ g)(4).

Back

(f ∘ g)(4) = f(g(4)) = f(4/2) = f(2) = 3(2) - 5 = 1.