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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![**Problem: Find the Inverse of a Function**
Given the function:
\[ h(x) = \frac{3}{x} + 2 \]
**Select the correct inverse function from the options below:**
**A.** \[ \frac{2}{x-2} \]
**B.** \[ \frac{3}{x+2} \]
**C.** \[ \frac{2}{x+3} \]
**D.** \[ \frac{3}{x-2} \]
**E.** \[ \frac{2}{x-3} \]
To determine the inverse of a function, we follow these steps:
1. Replace \( h(x) \) with \( y \).
2. Swap \( x \) and \( y \).
3. Solve for \( y \) to find the inverse function \( h^{-1}(x) \).
For the given function \( h(x) = \frac{3}{x} + 2 \):
1. Start with \( y = \frac{3}{x} + 2 \).
2. Swap \( x \) and \( y \) to get \( x = \frac{3}{y} + 2 \).
3. Solve for \( y \):
\[ x - 2 = \frac{3}{y} \]
\[ y = \frac{3}{x - 2} \]
Thus, the inverse function \( h^{-1}(x) \) is \( \frac{3}{x - 2} \).
The correct answer is **D: \(\frac{3}{x-2}\)**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16026111-938d-475f-a906-01f519f5a5a9%2F354589cc-f7a6-4606-b7ef-2160a4088fa6%2Fu9pksu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Find the Inverse of a Function**
Given the function:
\[ h(x) = \frac{3}{x} + 2 \]
**Select the correct inverse function from the options below:**
**A.** \[ \frac{2}{x-2} \]
**B.** \[ \frac{3}{x+2} \]
**C.** \[ \frac{2}{x+3} \]
**D.** \[ \frac{3}{x-2} \]
**E.** \[ \frac{2}{x-3} \]
To determine the inverse of a function, we follow these steps:
1. Replace \( h(x) \) with \( y \).
2. Swap \( x \) and \( y \).
3. Solve for \( y \) to find the inverse function \( h^{-1}(x) \).
For the given function \( h(x) = \frac{3}{x} + 2 \):
1. Start with \( y = \frac{3}{x} + 2 \).
2. Swap \( x \) and \( y \) to get \( x = \frac{3}{y} + 2 \).
3. Solve for \( y \):
\[ x - 2 = \frac{3}{y} \]
\[ y = \frac{3}{x - 2} \]
Thus, the inverse function \( h^{-1}(x) \) is \( \frac{3}{x - 2} \).
The correct answer is **D: \(\frac{3}{x-2}\)**.
![**Graph Analysis: Function Verification**
Text:
The following graph is the graph of a function.
[Graph Description]:
- The graph displays a curve on a Cartesian plane.
- The curve passes through the origin and splits into two branches:
- One branch is in the first quadrant, curving upwards to the right.
- The other branch is in the third quadrant, curving downwards to the left.
Select one:
- True
- False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16026111-938d-475f-a906-01f519f5a5a9%2F354589cc-f7a6-4606-b7ef-2160a4088fa6%2Fjorcvj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Analysis: Function Verification**
Text:
The following graph is the graph of a function.
[Graph Description]:
- The graph displays a curve on a Cartesian plane.
- The curve passes through the origin and splits into two branches:
- One branch is in the first quadrant, curving upwards to the right.
- The other branch is in the third quadrant, curving downwards to the left.
Select one:
- True
- False
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