Operations of Functions and Composition of Functions

Front

What is the definition of a function?

Back

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

Front

What does it mean to evaluate a function at a specific point?

Back

To evaluate a function at a specific point means to substitute that point into the function's equation and calculate the output.

Front

Find f(2) if f(x) = 3x - 9.

Back

f(2) = 3(2) - 9 = 6 - 9 = -3.

Front

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

Back

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

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f + g)(x).

Back

(f + g)(x) = 5x^2 + 6x - 1.

Front

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

Back

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

Front

Given f(x) = 3x^2 + 7x and g(x) = 2x^2 - x - 1, find (f - g)(x).

Back

(f - g)(x) = x^2 + 8x + 1.

Front

What does it mean to multiply two functions f(x) and g(x)?

Back

To multiply two functions, (f * g)(x), is defined as f(x) * g(x).

Front

Given f(x) = 2x + 4 and g(x) = 3x^2 - 1, find f(x) * g(x).

Back

f(x) * g(x) = 6x^3 + 12x^2 - 2x - 4.

Front

What is the composition of functions f and g, denoted as g(f(x))?

Back

The composition g(f(x)) means to substitute f(x) into g(x).