Function operations

Front

What is function subtraction and how is it performed?

Back

Function subtraction involves taking two functions, f(x) and g(x), and subtracting g(x) from f(x). The result is a new function defined as (f - g)(x) = f(x) - g(x).

Front

How do you find the composition of two functions, f(g(x))?

Back

To find the composition of two functions, substitute g(x) into f(x). This means you replace every instance of x in f(x) with g(x).

Front

What is the product of two functions, f(x) and g(x)?

Back

The product of two functions is defined as (f ⋅ g)(x) = f(x) * g(x). This results in a new function that is the product of the outputs of f and g for the same input x.

Front

What is the quotient of two functions, f(x) and g(x)?

Back

The quotient of two functions is defined as (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0. This results in a new function that is the division of the outputs of f and g for the same input x.

Front

What is the significance of simplifying expressions in function operations?

Back

Simplifying expressions helps to make calculations easier and clearer, allowing for easier evaluation and understanding of the function's behavior.

Front

How do you evaluate a function at a specific value, such as x = 10?

Back

To evaluate a function at a specific value, substitute the value into the function's expression and simplify to find the output.

Front

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

Back

The result is f(x) - g(x) = x^2 - x + 18.

Front

What is the result of f(g(x)) when f(x) = 3x + 10 and g(x) = x - 2?

Back

The result is f(g(x)) = 3(x - 2) + 10 = 3x + 4.

Front

How do you find the product f(x) ⋅ g(x) for f(x) = 2x + 4 and g(x) = 3x^2 - 1?

Back

The product is f(x) ⋅ g(x) = (2x + 4)(3x^2 - 1) = 6x^3 + 12x^2 - 2x - 4.

Front

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

Back

The result is f(g(x)) = 2(x^2 + 3) = 2x^2 + 6.