Composition of Functions

Front

What is the composition of functions?

Back

The composition of functions is a process where one function is applied to the result of another function. It is denoted as (f◦g)(x) = f(g(x)).

Front

If f(x) = 2x and g(x) = x + 3, what is (f◦g)(x)?

Back

(f◦g)(x) = f(g(x)) = f(x + 3) = 2(x + 3) = 2x + 6.

Front

What is the formula for (f⋅g)(x)?

Back

The formula for (f⋅g)(x) is f(x) * g(x), which means you multiply the outputs of both functions.

Front

If f(x) = x^2 and g(x) = 3x, what is (g◦f)(x)?

Back

(g◦f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2.

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 f(x) = x + 1 and g(x) = 2x, what is (f◦g)(2)?

Back

(f◦g)(2) = f(g(2)) = f(2*2) = f(4) = 4 + 1 = 5.

Front

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

Back

(f◦g)(x) is the composition of functions, while (f⋅g)(x) is the product of the functions.

Front

If f(x) = 3x - 2 and g(x) = x^2, what is (f◦g)(x)?

Back

(f◦g)(x) = f(g(x)) = f(x^2) = 3(x^2) - 2 = 3x^2 - 2.

Front

What is the output of f(g(5)) if f(x) = 2x + 1 and g(x) = x - 3?

Back

g(5) = 5 - 3 = 2; f(g(5)) = f(2) = 2*2 + 1 = 5.

Front

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

Back

(g◦f)(x) = g(f(x)) = g(x^3) = x^3 + 1.