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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![### Understanding Inverse Functions: Finding \( h^{-1}(x) \)
In this exercise, we are given a function \( h(x) = 4x - 3 \) and are required to find the equation for the inverse function \( h^{-1}(x) \). Below are the options provided:
#### Question:
If \( h(x) = 4x - 3 \), what is an equation for \( h^{-1}(x) \)?
#### Options:
- A. \( h^{-1}(x) = 3x + 4 \)
- B. \( h^{-1}(x) = 3x - 4 \)
- C. \( h^{-1}(x) = \frac{x + 3}{4} \)
- D. \( h^{-1}(x) = \frac{x - 3}{4} \)
### Detailed Breakdown:
To find the inverse function \( h^{-1}(x) \), follow these steps:
1. **Write the given function**:
\( h(x) = 4x - 3 \)
2. **Replace \( h(x) \) with \( y \)**:
\( y = 4x - 3 \)
3. **Solve for \( x \) in terms of \( y \)**:
\[
y = 4x - 3
\]
Add 3 to both sides:
\[
y + 3 = 4x
\]
Divide by 4:
\[
x = \frac{y + 3}{4}
\]
4. **Replace \( y \) with \( x \)** to get the inverse function::
\[
h^{-1}(x) = \frac{x + 3}{4}
\]
Hence, the correct answer is Option C:
\[
h^{-1}(x) = \frac{x + 3}{4}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c8ca9d4-5160-4b26-bb14-23f02588e445%2Fcbca7bb9-9d10-44fb-970a-e35819b21d91%2F0qr9jaf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Inverse Functions: Finding \( h^{-1}(x) \)
In this exercise, we are given a function \( h(x) = 4x - 3 \) and are required to find the equation for the inverse function \( h^{-1}(x) \). Below are the options provided:
#### Question:
If \( h(x) = 4x - 3 \), what is an equation for \( h^{-1}(x) \)?
#### Options:
- A. \( h^{-1}(x) = 3x + 4 \)
- B. \( h^{-1}(x) = 3x - 4 \)
- C. \( h^{-1}(x) = \frac{x + 3}{4} \)
- D. \( h^{-1}(x) = \frac{x - 3}{4} \)
### Detailed Breakdown:
To find the inverse function \( h^{-1}(x) \), follow these steps:
1. **Write the given function**:
\( h(x) = 4x - 3 \)
2. **Replace \( h(x) \) with \( y \)**:
\( y = 4x - 3 \)
3. **Solve for \( x \) in terms of \( y \)**:
\[
y = 4x - 3
\]
Add 3 to both sides:
\[
y + 3 = 4x
\]
Divide by 4:
\[
x = \frac{y + 3}{4}
\]
4. **Replace \( y \) with \( x \)** to get the inverse function::
\[
h^{-1}(x) = \frac{x + 3}{4}
\]
Hence, the correct answer is Option C:
\[
h^{-1}(x) = \frac{x + 3}{4}
\]
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