Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f ∘ g)(x) = 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 formula for finding (f ∘ g)(x)?

Back

(f ∘ g)(x) = f(g(x)).

Front

If p(x) = 3x + 4, what is p(p(1))?

Back

p(p(1)) = p(3(1) + 4) = p(7) = 3(7) + 4 = 25.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if (f ∘ g)(x) = x and (g ∘ f)(x) = x for all x in the domain.

Front

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

Back

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

Front

What is the result of p(q(x)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

p(q(x)) = p(2x^2) = 3(2x^2) + 4 = 6x^2 + 4.

Front

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

Back

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

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 may yield different results.

Front

If g(x) = 6x + 4 and f(x) = 2x - 7, find f(x) * g(x).

Back

f(x) * g(x) = (2x - 7)(6x + 4) = 12x^2 - 28x - 42.