LT 14 Operations of functions

Front

What is the definition of function operations?

Back

Function operations refer to the ways in which two or more functions can be combined to create new functions, including addition, subtraction, multiplication, and division.

Front

What is the formula for the product of two functions, (g*f)(x)?

Back

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

Front

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

Back

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

Front

What is the formula for the difference of two functions, (g-f)(x)?

Back

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

Front

What is the definition of a constant function?

Back

A constant function is a function that always returns the same value regardless of the input, represented as f(x) = c, where c is a constant.

Front

If g(x) = 2x + 3 and f(x) = 4, what is (g*f)(x)?

Back

(g*f)(x) = g(x) * f(x) = (2x + 3) * 4 = 8x + 12.

Front

If g(x) = x^2 and f(x) = 3x, what is (g+f)(x)?

Back

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

Front

What is the value of (g*f)(x) if g(x) = 5 and f(x) = x + 1?

Back

(g*f)(x) = g(x) * f(x) = 5 * (x + 1) = 5x + 5.

Front

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

Back

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

Front

If g(x) = 4 and f(x) = x^2, what is (g*f)(x)?

Back

(g*f)(x) = g(x) * f(x) = 4 * x^2 = 4x^2.