EXIT Operations on Functions

Front

What is the definition of function subtraction?

Back

Function subtraction is the operation of subtracting one function from another, denoted as (f - g)(x) = f(x) - g(x).

Front

How do you find (f - g)(x) for f(x) = 3x² + 7x and g(x) = 2x² - x - 1?

Back

(f - g)(x) = (3x² + 7x) - (2x² - x - 1) = x² + 8x + 1.

Front

What is the definition of function addition?

Back

Function addition is the operation of adding two functions together, denoted as (f + g)(x) = f(x) + g(x).

Front

How do you find (f + g)(x) for f(x) = 3x² + 7x and g(x) = 2x² - x - 1?

Back

(f + g)(x) = (3x² + 7x) + (2x² - x - 1) = 5x² + 6x - 1.

Front

What does f(2) represent?

Back

f(2) represents the value of the function f at x = 2.

Front

Calculate f(2) for f(x) = x + 2.

Back

f(2) = 2 + 2 = 4.

Front

What is the process to evaluate f(3) + g(2) for f(x) = x + 2 and g(x) = 5x - 1?

Back

First, find f(3) = 3 + 2 = 5 and g(2) = 5(2) - 1 = 9. Then, f(3) + g(2) = 5 + 9 = 14.

Front

What does f(-1) represent?

Back

f(-1) represents the value of the function f at x = -1.

Front

Calculate f(-1) for f(x) = 3x² + 7x.

Back

f(-1) = 3(-1)² + 7(-1) = 3 - 7 = -4.

Front

What is the significance of the term 'function'?

Back

A function is a relation that assigns exactly one output for each input from its domain.