LT 34 Inverse of a function

Front

What is the inverse of the function f(x) = -4x - 12?

Back

f⁻¹(x) = -1/4x - 3

Front

What is the inverse of the points (1,3)(2,4)(6,8)?

Back

(3,1)(4,2)(8,6)

Front

What does it mean for two functions to be inverse functions?

Back

They are functions that 'undo' each other, meaning f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

If f(x) = 3x - 9, what is f⁻¹(12)?

Back

7

Front

What is the graphical representation of inverse functions?

Back

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

Front

What is the condition for a function to have an inverse?

Back

A function must be one-to-one (bijective) to have an inverse.

Front

What is the inverse of the function f(x) = x² for x ≥ 0?

Back

f⁻¹(x) = √x.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the inverse of the function f(x) = -x + 5?

Back

f⁻¹(x) = -x + 5.