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(x) and g(x) are two functions, then the composition of f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

If g(x) = 3x + 4 and h(x) = 3x - 1, what is g(h(x))?

Back

g(h(x)) = 9x + 1.

Front

What is the formula for adding two functions f and g?

Back

(f + g)(x) = f(x) + g(x).

Front

If f(x) = 3x^2 + 1 and g(x) = 4x + 5, what is (f + g)(2)?

Back

(f + g)(2) = 26.

Front

What is the result of g(f(x)) if f(x) = x - 1 and g(x) = 2x?

Back

g(f(x)) = 2x - 2.

Front

How do you evaluate f(x - 2) if f(x) = 2x^2 - 5x + 12?

Back

f(x - 2) = 2(x - 2)^2 - 5(x - 2) + 12 = 2x^2 - 13x + 18.

Front

What is the value of f(g(5)) if f(x) = 3x + 10 and g(x) = x - 2?

Back

f(g(5)) = 19.

Front

What is the difference between f(g(x)) and g(f(x))?

Back

f(g(x)) applies g first and then f, while g(f(x)) applies f first and then g.

Front

What is the identity function?

Back

The identity function is a function that always returns the same value that was used as its input. It is denoted as I(x) = x.

Front

What is the composition of the identity function with another function f?

Back

(I ∘ f)(x) = f(x) and (f ∘ I)(x) = f(x).