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, denoted as (f ° g)(x) = f(g(x)).

Front

If f(x) = 2x + 3 and g(x) = x - 1, what is (f ° g)(2)?

Back

(f ° g)(2) = f(g(2)) = f(1) = 2(1) + 3 = 5.

Front

Define the term 'domain' in the context of functions.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

If p(x) = x^2 and q(x) = 3x, find p(q(1)).

Back

p(q(1)) = p(3) = 3^2 = 9.

Front

What does it mean for two functions to be 'inverse functions'?

Back

Two functions f and g are inverse functions if (f ° g)(x) = x and (g ° f)(x) = x for all x in the domain.

Front

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

Back

(g ° f)(3) = g(f(3)) = g(5) = 5^2 = 25.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is (f ° g)(x), which means f(g(x)).

Front

If f(x) = 4x - 1 and g(x) = x/2, find (f ° g)(4).

Back

(f ° g)(4) = f(g(4)) = f(2) = 4(2) - 1 = 7.

Front

What is the output of the function g(x) = 2x + 1 when the input is x = 0?

Back

g(0) = 2(0) + 1 = 1.