Function Operations & Compositions of Functions

Front

Define function addition.

Back

Function addition is the operation of combining two functions, f(x) and g(x), to create a new function (f + g)(x) = f(x) + g(x).

Front

What is the formula for function multiplication?

Back

Function multiplication is defined as (f ⋅ g)(x) = f(x) * g(x).

Front

Given f(x) = 2x and g(x) = x^2 + 3, find (f + g)(x).

Back

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

Front

What is function composition?

Back

Function composition is the operation of applying one function to the results of another, denoted as (g ° f)(x) = g(f(x)).

Front

Calculate (f ° g)(x) if f(x) = x - 5 and g(x) = 3x^2 - 1.

Back

(f ° g)(x) = g(f(x)) = g(x - 5) = 3(x - 5)^2 - 1 = 3x^2 - 30x + 74.

Front

What is the result of (f + g)(x) for f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1?

Back

(f + g)(x) = (3x^2 + 7x) + (2x^2 - x - 1) = 5x^2 + 6x - 1.

Front

If f(x) = 3x^2 - 2x + 1 and g(x) = x - 4, find (f ⋅ g)(x).

Back

(f ⋅ g)(x) = (3x^2 - 2x + 1)(x - 4) = 3x^3 - 14x^2 + 9x - 4.

Front

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

Back

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

Front

Find (f ° g)(x) for f(x) = 2x and g(x) = x^2 + 3.

Back

(f ° g)(x) = f(g(x)) = f(x^2 + 3) = 2(x^2 + 3) = 2x^2 + 6.

Front

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

Back

(f + g)(x) is the sum of the functions, while (f ⋅ g)(x) is the product of the functions.