Inverse Functions

Front

What is 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

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. The resulting equation is the inverse function.

Front

What is the inverse of f(x) = 2x + 3?

Back

f^-1(x) = (x - 3)/2.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are reflections of each other across the line y = x.

Front

If f(a) = b, what is f^-1(b)?

Back

f^-1(b) = a.

Front

What is the inverse of the coordinates (4, 5)?

Back

The inverse is (5, 4).

Front

How can you verify if two functions are inverses?

Back

To verify, check if f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What does it mean if a function is one-to-one?

Back

A one-to-one function means that each output is produced by exactly one input, allowing for an inverse to exist.

Front

What is the inverse of f(x) = x² for x ≥ 0?

Back

f^-1(x) = √x.

Front

What is the first step to find the inverse of f(x) = 3x - 5?

Back

Replace f(x) with y: y = 3x - 5.