Function Review

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f^-1(y) takes y back to x.

Front

What line is the inverse of a function reflected over?

Back

The inverse of a function is reflected over the line y = x.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function f(x) = ax + b, swap x and y, then solve for y.

Front

What is the inverse of f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3.

Front

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

Back

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

Front

Given f(x) = 3x² + 7x and g(x) = 2x² - x - 1, what is (f + g)(x)?

Back

(f + g)(x) = 5x² + 6x - 1.

Front

What does it mean for two functions to be inverses of each other?

Back

Two functions are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

How do you find the composition of two functions f(g(x))?

Back

To find f(g(x)), substitute g(x) into f(x).

Front

Given f(x) = 2x and g(x) = x² + 3, what is f(g(x))?

Back

f(g(x)) = 2x² + 6.

Front

What is the definition of a function?

Back

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