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, switch the x and y in the equation and solve for y.

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function becomes the range of its inverse, and vice versa.

Front

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

Back

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

Front

If f(x) = 2x + 3, what is f^(-1)(x)?

Back

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

Front

What is the graphical representation of inverse functions?

Back

Inverse functions are reflections of each other over the line y = x.

Front

If f(2) = 5, what is f^(-1)(5)?

Back

f^(-1)(5) = 2.

Front

What is the significance of the point (a, b) in relation to inverse functions?

Back

If (a, b) is a point on the function f, then (b, a) is a point on its inverse f^(-1).

Front

How do you verify if two functions are inverses?

Back

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

Front

What is the inverse of the function f(x) = x^2 for x >= 0?

Back

f^(-1)(x) = √x.