IM3 LT20 Find Inverse of a function algebraically & graphically

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, meaning if f(x) = y, then f^-1(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap x and y in the equation and solve for y.

Front

What is the notation for the inverse of a function f(x)?

Back

The inverse of the function f(x) is written as f^-1(x).

Front

What does it mean to switch x's and y's in a function?

Back

Switching x's and y's means that for every point (a, b) on the graph of the function, the point (b, a) will be on the graph of its inverse.

Front

What is the graphical representation of an inverse function?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

If g(x) = f^-1(x), what does this imply about the relationship between f and g?

Back

It implies that g is the inverse function of f, meaning g(f(x)) = x and f(g(x)) = x.

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as the line of reflection for the graphs of a function and its inverse.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse unless it is not a one-to-one function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.

Front

How can you verify if two functions are inverses of each other?

Back

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