2024 -25 FLASHCARD Inverse Functions

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

Are the following functions inverses of each other? f(x) = 2x + 3 and f^-1(x) = (x - 3)/2

Back

Inverse Functions

Front

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

Back

(4, 1) and (6, 4)

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that f(f^-1(x)) = x.

Front

How do you find the inverse of a linear function?

Back

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

Front

What is the graphical representation of inverse functions?

Back

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

Front

What is the condition for two functions to be inverses?

Back

f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

Find the inverse of f(x) = 5x + 2.

Back

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