Inverses and Composition of Functions

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 the composition of functions?

Back

The composition of functions f and g, denoted as (f ° g)(x), is defined as f(g(x)). It means applying g first and then applying f to the result.

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes x to y, then the inverse function f⁻¹(y) takes y back to x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function, replace f(x) with y, swap x and y, and then solve for y.

Front

What is the notation for the inverse of a function?

Back

The notation for the inverse of a function f is f⁻¹.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

For f(x) = x², what is the range?

Back

The range is [0, ∞) since x² is always non-negative.

Front

What does it mean for two functions to be inverses?

Back

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