Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect 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, replace f(x) with y, swap x and y, and then solve for y.

Front

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

Back

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

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because f(g(x)) = x and g(f(x)) = x.

Front

What is the graphical representation of inverse functions?

Back

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

Front

What is the condition for two functions to be inverses?

Back

For two functions f and g to be inverses, f(g(x)) = x and g(f(x)) = x must hold true for all x in the domain.

Front

Find the inverse of f(x) = 3x - 5.

Back

f^-1(x) = (x + 5)/3.

Front

Find the inverse of f(x) = -4x - 12.

Back

f^-1(x) = -1/4x - 3.

Front

What is the inverse of a constant function?

Back

A constant function does not have an inverse because it does not pass the horizontal line test.

Front

What does it mean if a function is not one-to-one?

Back

If a function is not one-to-one, it means that there are at least two different inputs that produce the same output, making it impossible to find an inverse.