Function Composition

Front

What is function composition?

Back

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

Front

How do you find (g ∘ f)(x)?

Back

To find (g ∘ f)(x), first evaluate f(x), then substitute that result into g. This means you compute g(f(x)).

Front

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

Back

g(f(-1)) = g(2(-1)) = g(-2) = 2(-2)^2 - 1 = 8 - 1 = 7.

Front

What is the formula for the weight of a tank in terms of time if V = 9 - t and W = 2V?

Back

W = 2(9 - t) = 18 - 2t.

Front

What does f(g(x)) represent?

Back

f(g(x)) represents the composition of functions f and g, where g is applied first, followed by f.

Front

If f(x) = 1/3 x, what is f(g(x)) if g(x) = 3x?

Back

f(g(x)) = f(3x) = 1/3(3x) = x.

Front

What is the output of (g ∘ f)(2) if g(f(2)) = -1.75?

Back

The output of (g ∘ f)(2) is -1.75.

Front

How do you express W in terms of t if V = 9 - t?

Back

W = 2V = 2(9 - t) = 18 - 2t.

Front

What is the significance of the notation (f ∘ g)(x)?

Back

The notation (f ∘ g)(x) signifies that function g is applied to x first, and then function f is applied to the result of g.

Front

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

Back

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