Function Composition Practice

Front

What is 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 evaluate f(g(x))?

Back

To evaluate f(g(x)), first find the value of g(x) for a given x, and then substitute that value into the function f.

Front

What is the notation for function composition?

Back

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

Front

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

Back

(f ∘ g)(2) = f(g(2)) = f(2^2) = f(4) = 2(4) + 1 = 9.

Front

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

Back

g(f(1)) = g(1 + 3) = g(4) = 2(4) = 8.

Front

What does it mean if (f ∘ g)(x) = x?

Back

If (f ∘ g)(x) = x, then g is the inverse function of f, meaning f and g undo each other.

Front

How do you find the inverse of a function?

Back

To find the inverse of a function f(x), swap x and y in the equation and solve for y. The result is f^(-1)(x).

Front

If h(x) = 3x - 5, what is h(2)?

Back

h(2) = 3(2) - 5 = 6 - 5 = 1.

Front

What is the domain of a composite function?

Back

The domain of a composite function (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 k(x) = x/2, what is (k ∘ k)(4)?

Back

(k ∘ k)(4) = k(k(4)) = k(4/2) = k(2) = 2/2 = 1.