Functions and compositions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is function composition?

Back

Function composition is the process of applying one function to the results of another function. If f and g are functions, then the composition of f and g is denoted as f(g(x)).

Front

How do you find f(g(x))?

Back

To find f(g(x)), first evaluate g(x) for a given x, then substitute that result into f.

Front

What is the inverse of a function?

Back

The inverse of a function f(x) 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 f(x) = 1/4x - 7?

Back

To find the inverse, swap x and y, then solve for y: y = 1/4x - 7 becomes x = 1/4y - 7, leading to f^(-1)(x) = 4x + 28.

Front

What is the sum of two functions?

Back

The sum of two functions f and g, denoted (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 product of two functions?

Back

The product of two functions f and g, denoted (f * g)(x), is defined as f(x) * g(x).

Front

How do you find f(g(0)) for f(x) = 3x + 10 and g(x) = x - 2?

Back

First, find g(0) = 0 - 2 = -2, then substitute into f: f(-2) = 3(-2) + 10 = 4.

Front

What is the difference of two functions?

Back

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