Find the inverse of the function k = 97v² , which represents the kinetic energy k (in joules) of a 194- ,2 kilogram object traveling at speed v (in meters per second). Assume v> 0.
Find the inverse of the function k = 97v² , which represents the kinetic energy k (in joules) of a 194- ,2 kilogram object traveling at speed v (in meters per second). Assume v> 0.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Finding the Inverse of a Function: Kinetic Energy**
To better understand the relationship between kinetic energy and speed, let's find the inverse of the given function. The function provided is:
\[ k = 97v^2 \]
Here, \( k \) represents the kinetic energy (in joules) of a 194-kilogram object traveling at speed \( v \) (in meters per second). Assume \( v \geq 0 \).
### Steps to Finding the Inverse
1. **Express the Function**:
The function is \( k = 97v^2 \).
2. **Swap \( k \) and \( v \)**:
To find the inverse, swap \( k \) and \( v \) in the equation:
\[ v = 97k^2 \]
3. **Solve for \( v \)**:
Taking the square root of both sides to solve for \( v \), we get:
\[ v = \sqrt{\frac{k}{97}} \]
Since \( v \geq 0 \), we only consider the positive root.
4. **Express the Inverse Function**:
The inverse function is:
\[ v = \sqrt{\frac{k}{97}} \]
Thus, the inverse function is \( v = \sqrt{\frac{k}{97}} \).
This inverse function allows you to determine the speed \( v \) of the object if you know the kinetic energy \( k \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a18a320-2046-4089-b27e-0ca38db1d2b2%2F6dfbf59b-5b29-4073-9bfd-f7171f9aa4c5%2Fnkz3lc.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Inverse of a Function: Kinetic Energy**
To better understand the relationship between kinetic energy and speed, let's find the inverse of the given function. The function provided is:
\[ k = 97v^2 \]
Here, \( k \) represents the kinetic energy (in joules) of a 194-kilogram object traveling at speed \( v \) (in meters per second). Assume \( v \geq 0 \).
### Steps to Finding the Inverse
1. **Express the Function**:
The function is \( k = 97v^2 \).
2. **Swap \( k \) and \( v \)**:
To find the inverse, swap \( k \) and \( v \) in the equation:
\[ v = 97k^2 \]
3. **Solve for \( v \)**:
Taking the square root of both sides to solve for \( v \), we get:
\[ v = \sqrt{\frac{k}{97}} \]
Since \( v \geq 0 \), we only consider the positive root.
4. **Express the Inverse Function**:
The inverse function is:
\[ v = \sqrt{\frac{k}{97}} \]
Thus, the inverse function is \( v = \sqrt{\frac{k}{97}} \).
This inverse function allows you to determine the speed \( v \) of the object if you know the kinetic energy \( k \).
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