Composite Functions Review

Front

Define a composite function.

Back

A composite function is a function that is formed by combining two functions, where the output of one function becomes the input of the other. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the notation for composite functions?

Back

The notation for composite functions is (f ∘ g)(x), which means f(g(x)).

Front

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

Back

(g ∘ h)(2) = g(h(2)) = g(2^2) = g(4) = 2(4) + 3 = 11.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) is a function that reverses the effect of f. If f(x) = y, then the inverse function f^(-1)(y) = x.

Front

How do you determine if two functions are 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

Calculate h(g(-3)) if h(x) = x^2 + 2 and g(x) = 3x - 1.

Back

h(g(-3)) = h(3(-3) - 1) = h(-10) = (-10)^2 + 2 = 102.

Front

What is the composition of functions g(t) = 4t - 2 and h(t) = t^2 + t?

Back

(g ∘ h)(t) = g(h(t)) = g(t^2 + t) = 4(t^2 + t) - 2 = 4t^2 + 4t - 2.

Front

Find (f ∘ g)(t) if f(t) = -t + 5 and g(t) = 3t + 3.

Back

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

Front

What is the output of g(h(-3)) if g(t) = 4t - 2 and h(t) = t^2 + t?

Back

g(h(-3)) = g((-3)^2 + (-3)) = g(6) = 4(6) - 2 = 22.

Front

Explain the process of finding composite functions step by step.

Back

1. Identify the inner function and the outer function. 2. Evaluate the inner function for the given input. 3. Substitute the result into the outer function. 4. Simplify to find the final output.