Composition of Functions

Front

What is a function composition?

Back

Function composition is the process of applying one function to the results of another function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find g(f(x)) if g(x) = x^2 + 6 and f(x) = 2x - 4?

Back

To find g(f(x)), substitute f(x) into g: g(f(x)) = g(2x - 4) = (2x - 4)^2 + 6 = 4x^2 - 16x + 22.

Front

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

Back

First, find g(2): g(2) = 3(2) + 2 = 8. Then, find f(8): f(8) = 2(8^2) - 1 = 127.

Front

How do you add two functions f(x) and g(x)?

Back

To add two functions, simply combine their outputs: (f + g)(x) = f(x) + g(x).

Front

What is the result of f(x) + g(x) if f(x) = 9 - 3x and g(x) = 5x - 7?

Back

f(x) + g(x) = (9 - 3x) + (5x - 7) = 2x + 2.

Front

How do you find g(f(x)) if f(x) = 2x^2 - 1 and g(x) = 3x + 2?

Back

Substitute f(x) into g: g(f(x)) = g(2x^2 - 1) = 3(2x^2 - 1) + 2 = 6x^2 - 1.

Front

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

Back

The difference of two functions is found by subtracting their outputs: (f - g)(x) = f(x) - g(x).

Front

What is the result of f(x) - g(x) if f(x) = x^2 + 9 and g(x) = x - 9?

Back

f(x) - g(x) = (x^2 + 9) - (x - 9) = x^2 - x + 18.

Front

What is the notation for function composition?

Back

Function composition is denoted as (f ∘ g)(x) or f(g(x)).

Front

What is the output of g(f(x)) if f(x) = 2x - 4 and g(x) = x^2 + 6?

Back

g(f(x)) = g(2x - 4) = (2x - 4)^2 + 6 = 4x^2 - 16x + 22.