2024 -25 FLASHCARD Inverse Functions

Front

What is the definition of 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

Find the inverse of f(x) = 1/4x - 7.

Back

f^-1(x) = 4x + 28.

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(1) = 4, what is f^-1(4)?

Back

f^-1(4) = 1.

Front

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

Back

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

Front

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

Back

Two functions are inverses if applying one function followed by the other returns the original input. That is, f(f^-1(x)) = x and f^-1(f(x)) = x.

Front

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

Back

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

Front

If f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

Back

f^-1(x) goes through (4, 1) and (6, 4).

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 across the line y = x.