Composition of Functions & Function Operations

Front

What is the composition of functions?

Back

The composition of functions is an operation that takes two functions, f and g, and produces a new function, denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the input value into the function's equation and simplify.

Front

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

Back

The difference f(x) - g(x) is calculated by subtracting g(x) from f(x), resulting in x^2 - x + 18.

Front

What does g(5) represent in function notation?

Back

g(5) represents the output of the function g when the input is 5.

Front

How do you evaluate g(4x)?

Back

To evaluate g(4x), substitute 4x into the function g and simplify the expression.

Front

What is the significance of function operations in mathematics?

Back

Function operations, such as addition, subtraction, multiplication, and composition, allow us to combine and manipulate functions to solve complex problems.

Front

What is the output of f[g(5)] if f(x) = 2x + 2 and g(5) = 375?

Back

To find f[g(5)], substitute g(5) into f: f(375) = 2(375) + 2 = 752.

Front

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

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 given by (f - g)(x) = f(x) - g(x).

Front

What is the product of two functions?

Back

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