Operations on Functions

Front

Define the operation of addition on functions.

Back

The addition of two functions f(x) and g(x) is defined as (f + g)(x) = f(x) + g(x).

Front

What is the formula for subtracting two functions?

Back

The subtraction of two functions f(x) and g(x) is defined as (f - g)(x) = f(x) - g(x).

Front

How do you find the product of two functions?

Back

The product of two functions f(x) and g(x) is defined as (f ⋅ g)(x) = f(x) * g(x).

Front

What is the quotient of two functions?

Back

The quotient of two functions f(x) and g(x) is defined as (f/g)(x) = f(x) / g(x), provided g(x) ≠ 0.

Front

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

Back

(f + g)(2) = (2(2) + 3) + ((2) - 1) = 7 + 1 = 8.

Front

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

Back

(f - g)(1) = (1^2) - (3(1)) = 1 - 3 = -2.

Front

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

Back

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

Front

Calculate (f/g)(-2) for f(x) = x^2 + 1 and g(x) = x + 3.

Back

(f/g)(-2) = ((-2)^2 + 1) / ((-2) + 3) = 5 / 1 = 5.

Front

Define the composition of functions.

Back

The composition of two functions f and g is defined as (f ∘ g)(x) = f(g(x)).

Front

If f(x) = x^2 and g(x) = 2x + 1, find (f ∘ g)(1).

Back

(f ∘ g)(1) = f(g(1)) = f(2(1) + 1) = f(3) = 3^2 = 9.