Composition of Functions Weekly HW

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. It is denoted as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = x - 4, what is f(2)?

Back

f(2) = 2 - 4 = -2.

Front

If g(x) = 8x - 2, what is g(2)?

Back

g(2) = 8(2) - 2 = 16 - 2 = 14.

Front

What does h(f(-2)) represent?

Back

It represents the value of function h applied to the result of function f evaluated at -2.

Front

If h(x) = -4x + 3, what is h(0)?

Back

h(0) = -4(0) + 3 = 3.

Front

What is the value of f(g(2)) if g(2) = 14?

Back

f(g(2)) = f(14) = 14 - 4 = 10.

Front

If f(x) = x - 4 and g(x) = 8x - 2, what is f(g(-1))?

Back

g(-1) = 8(-1) - 2 = -8 - 2 = -10; f(-10) = -10 - 4 = -14.

Front

What is the output of h(g(2))?

Back

h(g(2)) = h(14) = -4(14) + 3 = -56 + 3 = -53.

Front

If f(x) = x - 4, what is the inverse function f^(-1)(x)?

Back

f^(-1)(x) = x + 4.

Front

What is the significance of the order of functions in composition?

Back

The order matters because (f ∘ g)(x) is not necessarily equal to (g ∘ f)(x).