AP Calculus AB: 6.3.5 Finding the Inverse of a Function
This content explains how to find the inverse of a function both algebraically and graphically by switching the input and output variables. It also emphasizes verifying the inverse through composition, ensuring that both directions return the original input value.
Finding the Inverse of a Function
To determine the inverse of a function algebraically, swap the independent variable (x) and the dependent variable (y) and then solve for y.
Verify the inverse by composing it with the original function as described in the definition of an inverse.
Key Terms
Finding the Inverse of a Function
To determine the inverse of a function algebraically, swap the independent variable (x) and the dependent variable (y) and then solve for y...
note
To find the inverse of a function graphically, you
reflect the curve of the function across the line given
by y = x.T...
Which of the following correctly relates the process of algebraically finding the inverse of a function f (x)?
To find the inverse of a function, first rename the function y, then swap y and x, and solve for y to get an expression. If both f −1 ( f (x)) = x ...
Given f (x) = e^x + 2x, which of the following is
f −1 (1)?
0
Given f(x)=2x+3/x−1, find f−1(x).
f−1(x)=x+3/x−2
Given f(x)=1/x+2+5, where x≠−2,find f−1(x).
f−1(x)=1/x−5 −2
Related Flashcard Decks
Study Tips
- Press F to enter focus mode for distraction-free studying
- Review cards regularly to improve retention
- Try to recall the answer before flipping the card
- Share this deck with friends to study together
| Term | Definition |
|---|---|
Finding the Inverse of a Function |
|
note |
|
Which of the following correctly relates the process of algebraically finding the inverse of a function f (x)? | To find the inverse of a function, first rename the function y, then swap y and x, and solve for y to get an expression. If both f −1 ( f (x)) = x and f ( f −1 (x)) = x, this expression is f −1 (x). |
Given f (x) = e^x + 2x, which of the following is f −1 (1)? | 0 |
Given f(x)=2x+3/x−1, find f−1(x). | f−1(x)=x+3/x−2 |
Given f(x)=1/x+2+5, where x≠−2,find f−1(x). | f−1(x)=1/x−5 −2 |
To find the inverse of a one-to-one function f (x) graphically, reflect the function’s graph over ____________________. | y=x |
Given f (x) = 4x^ 5 + 1, find f −1 (x). | f−1(x)=5√x−1/4 |
Given f (x) = x ^2, for x > 0, find f −1 (x). | f−1(x)=√x |
Given ln(x−1)/3, find f−1(x). | f −1 (x) = e ^3x + 1 |
Given f (x) = ln (x^ 3 ), find f −1 (x). | f −1 (x) = e^ x / 3 |
Given f (x) = 2e ^3x + 8, find f −1 (x). | f−1(x)=1/3ln(x−8/2) |