Composition of Functions

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, denoted as (f ° g)(x) = f(g(x)).

Front

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

Back

(f ° g)(x) = f(g(x)) = f(x - 1) = 2(x - 1) + 3 = 2x - 2 + 3 = 2x + 1.

Front

What does f(g(5)) represent?

Back

f(g(5)) represents the value of the function f evaluated at the output of the function g when the input is 5.

Front

If f(x) = x - 5 and g(x) = 3x² - 1, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(3x² - 1) = (3x² - 1) - 5 = 3x² - 6.

Front

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

Back

f(g(5)) = f(5 - 2) = f(3) = 3(3) + 10 = 19.

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What is the notation for the composition of functions?

Back

The notation for the composition of functions is f(g(x)) or (f ° g)(x).

Front

If f(x) = 3x + 1 and g(x) = x², what is (f ° g)(2)?

Back

(f ° g)(2) = f(g(2)) = f(2²) = f(4) = 3(4) + 1 = 13.

Front

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

Back

f(g(5)) = f(5 + 3) = f(8) = 2(8) = 16.

Front

If f(x) = x + 4 and g(x) = 2x, what is (f ° g)(x)?

Back

(f ° g)(x) = f(g(x)) = f(2x) = 2x + 4.