Inverse function notation

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function g(y) = x.

Front

How do you denote the inverse of a function f?

Back

The inverse of a function f is denoted as f^(-1).

Front

What is the relationship between a function and its inverse?

Back

If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the difference between consecutive terms in an arithmetic sequence.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the ratio of consecutive terms in a geometric sequence.

Front

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, since f and g are inverse functions.

Front

How do you find the nth term of a sequence given its formula?

Back

Substitute n into the formula to calculate the nth term.

Front

What does it mean for two functions to be inverses?

Back

Two functions are inverses if they 'undo' each other, meaning applying one function followed by the other returns the original input.