Composite Functions Review

Front

Define composite functions.

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 of g of x'.

Front

If g(x) = -x and f(x) = 4x + 3, find g(f(x)).

Back

g(f(x)) = g(4x + 3) = - (4x + 3) = -4x - 3.

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 g(t) = 2t - 4 and f(t) = t + 1, find (g ∘ f)(t).

Back

(g ∘ f)(t) = g(f(t)) = g(t + 1) = 2(t + 1) - 4 = 2t + 2 - 4 = 2t - 2.

Front

If g(x) = 4x + 3 and h(x) = 3x^2 + 4, find g(h(x)).

Back

g(h(x)) = g(3x^2 + 4) = 4(3x^2 + 4) + 3 = 12x^2 + 16 + 3 = 12x^2 + 19.

Front

If f(t) = -t + 5 and g(t) = 3t + 3, find (f ∘ g)(t).

Back

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

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

How do you determine if two functions are inverses graphically?

Back

Two functions are inverses if their graphs are symmetric with respect to the line y = x.

Front

What is the range of a composite function?

Back

The range of a composite function (f ∘ g) is the set of all possible outputs f(g(x)) as x varies over the domain of g.