Adv Math -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 (f ∘ g)(x) = f(g(x)).

Front

How do you denote the composition of two functions f and g?

Back

The composition of two functions f and g is denoted as (f ∘ g)(x).

Front

If f(x) = 2x^2 - 1, what is f(3)?

Back

f(3) = 2(3)^2 - 1 = 17.

Front

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

Back

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

Front

What is the value of (f ∘ g)(-1) if f(x) = 2x^2 - 1 and g(x) = \frac{1}{x^2}?

Back

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

Front

What is the value of g(f(5)) if f(x) = 2x^2 - 1 and g(x) = 3x + 2?

Back

g(f(5)) = g(49) = 3(49) + 2 = 149.

Front

If h(x) = x + 6, what is h(f(g(2)))?

Back

h(f(g(2))) = h(f(8)) = h(15) = 21.

Front

What is the value of (g ∘ g)(-4) if g(x) = 3x + 2?

Back

(g ∘ g)(-4) = g(g(-4)) = g(-10) = -28.

Front

What is the domain of the function g(x) = \frac{1}{x^2}?

Back

The domain of g(x) is all real numbers except x = 0.

Front

What is the range of the function f(x) = 2x^2 - 1?

Back

The range of f(x) is all real numbers greater than or equal to -1.