Function Operations, Compositions, and Inverses

Front

Define function operations in mathematics.

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 function composition?

Back

Front

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

Back

The sum of two functions is found by adding their outputs: (f + g)(x) = f(x) + g(x).

Front

What is the formula for the difference of two functions?

Back

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

Front

How do you multiply two functions, f(x) and g(x)?

Back

The product of two functions is found by multiplying their outputs: (f * g)(x) = f(x) * g(x).

Front

What is the formula for the quotient of two functions?

Back

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

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's expression.

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^(-1), is a function that reverses the effect of f. If f(x) = y, then f^(-1)(y) = x.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, swap the x and y variables and solve for y.

Front

What is the significance of the composition of functions?

Back

The composition of functions allows for the chaining of operations, where the output of one function becomes the input of another.