Function Operations

Front

What is function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, denoted as (f - g)(x) = f(x) - g(x).

Front

Given f(x) = 2x + 3 and g(x) = x - 1, find (g - f)(x).

Back

(g - f)(x) = (x - 1) - (2x + 3) = -x - 4.

Front

What is function addition?

Back

Function addition is the operation of adding two functions together, denoted as (f + g)(x) = f(x) + g(x).

Front

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

Back

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

Front

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

Back

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

Front

Define the term 'function composition'.

Back

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

Front

If f(x) = x + 2 and g(x) = x^2, find (f ∘ g)(x).

Back

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

Front

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

Back

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

Front

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

Back

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

Front

What is the formula for finding (g - f)(x) if g(x) = 2x^2 and f(x) = x?

Back

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