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 and produces 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 relationship between a function and its inverse?

Back

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

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

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

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 graphical representation of an inverse function?

Back

The graph of an inverse function is obtained by reflecting the graph of the original function over the line y = x.

Front

How can you verify if two functions are inverses?

Back

To verify if two functions f and g are inverses, check if f(g(x)) = x and g(f(x)) = x for all x in their domains.

Front

What is the inverse of f(x) = 1/4x - 7?

Back

f⁻¹(x) = 4x + 28.

Front

If f(2) = 5, what is g(5) if g is the inverse of f?

Back

g(5) = 2.

Front

What points does the inverse function f⁻¹(x) pass through if f(x) passes through (a, b)?

Back

If f(a) = b, then f⁻¹(b) = a, meaning f⁻¹(x) passes through (b, a).