Function Operations Review

Front

What is the definition of function operations?

Back

Function operations involve combining two or more functions using addition, subtraction, multiplication, or division.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you find the quotient of two functions, g(x) and h(x)?

Back

To find the quotient g(x)/h(x), divide the output of g(x) by the output of h(x), ensuring h(x) ≠ 0.

Front

What is the domain restriction when dividing functions?

Back

The domain restriction is determined by the values that make the denominator zero, as these values are not allowed.

Front

What is the composition of functions?

Back

The composition of functions, denoted as (f ∘ g)(x), means applying function g first and then applying function f to the result.

Front

How do you evaluate q(p(-2)) if p(x) = 3x + 4 and q(x) = 2x^2?

Back

First, find p(-2) = 3(-2) + 4 = -2. Then, substitute -2 into q: q(-2) = 2(-2)^2 = 8.

Front

What is the formula for subtracting two functions, f(x) and g(x)?

Back

The formula for subtracting two functions is (f - g)(x) = f(x) - g(x).

Front

How do you find the sum of two functions, f(n) and g(n)?

Back

To find the sum, use the formula (f + g)(n) = f(n) + g(n).

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 result of f(n) + g(n) if f(n) = n^2 + 4n and g(n) = -n - 5?

Back

f(n) + g(n) = (n^2 + 4n) + (-n - 5) = n^2 + 3n - 5.