The function f(x)= (5x+7)/(2x-5) is one to one. **Finding the Domain and Range of $ f^{-1} $****Step 1: Find the Domain of $ f^{-1} $**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- **A.** The domain is $\{ x | x \geq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **B.** The domain is $\{ x | x \leq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **C.** The domain is $\{ x | x \neq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **D.** The domain is the set of all real numbers.---**Step 2: Find the Range of $ f^{-1} $**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- **A.** The range is $\{ y | y \neq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **B.** The range is $\{ y | y \leq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **C.** The range is $\{ y | y \geq \, \_\_\_\} $. - (Type integers or fractions. Use a comma to separate answers as needed.) - **D.** The range is the set of all real numbers.---Please make your selections based on the function characteristics you're evaluating. **Mathematical Analysis: Exploring One-to-One Functions**Given the function $ f(x) = \frac{5x + 7}{2x - 5} $, which is one-to-one, we will:(a) Find its inverse and verify the result.(b) Determine the domain and range for both $ f $ and $ f^{-1} $.**Part (a): Finding the Inverse**Determine $ f^{-1}(x) = $ $[ \text{Answer Box} ]$ and simplify your answer.**Part (b): Determining the Domain of $ f $**Select the correct option for the domain:- **A.** The domain is $ \{ x \mid x \neq $ $[ \text{Answer Box} ] $ \}- **B.** The domain is $ \{ x \mid x \leq $ $[ \text{Answer Box} ] $ \}- **C.** The domain is $ \{ x \mid x \geq $ $[ \text{Answer Box} ] $ \}- **D.** The domain is the set of all real numbers.**Finding the Range of $ f $**Select the correct option for the range:- **A.** The range is $ \{ y \mid y \leq $ $[ \text{Answer Box} ] $ \}- **B.** The range is $ \{ y \mid y \neq $ $[ \text{Answer Box} ] $ \}- **C.** The range is $ \{ y \mid y \geq $ $[ \text{Answer Box} ] $ \}- **D.** The range is the set of all real numbers. Use integers or fractions as needed for the entries in the boxes.

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Answered: The function f(x)= (5x+7)/(2x-5) is one…

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The function f(x)= (5x+7)/(2x-5) is one to one.

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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Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Question

The function f(x)= (5x+7)/(2x-5) is one to one.

**Finding the Domain and Range of $ f^{-1} $**

**Step 1: Find the Domain of $ f^{-1} $**

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **A.** The domain is $\{ x | x \geq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **B.** The domain is $\{ x | x \leq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **C.** The domain is $\{ x | x \neq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **D.** The domain is the set of all real numbers.

---

**Step 2: Find the Range of $ f^{-1} $**

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **A.** The range is $\{ y | y \neq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **B.** The range is $\{ y | y \leq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **C.** The range is $\{ y | y \geq \, \_\_\_\} $.
- (Type integers or fractions. Use a comma to separate answers as needed.)

- **D.** The range is the set of all real numbers.

---

Please make your selections based on the function characteristics you're evaluating.

**Mathematical Analysis: Exploring One-to-One Functions**

Given the function $ f(x) = \frac{5x + 7}{2x - 5} $, which is one-to-one, we will:

(a) Find its inverse and verify the result.

(b) Determine the domain and range for both $ f $ and $ f^{-1} $.

**Part (a): Finding the Inverse**

Determine $ f^{-1}(x) = $ $[ \text{Answer Box} ]$ and simplify your answer.

**Part (b): Determining the Domain of $ f $**

Select the correct option for the domain:

- **A.** The domain is $ \{ x \mid x \neq $ $[ \text{Answer Box} ] $ \}
- **B.** The domain is $ \{ x \mid x \leq $ $[ \text{Answer Box} ] $ \}
- **C.** The domain is $ \{ x \mid x \geq $ $[ \text{Answer Box} ] $ \}
- **D.** The domain is the set of all real numbers.

**Finding the Range of $ f $**

Select the correct option for the range:

- **A.** The range is $ \{ y \mid y \leq $ $[ \text{Answer Box} ] $ \}
- **B.** The range is $ \{ y \mid y \neq $ $[ \text{Answer Box} ] $ \}
- **C.** The range is $ \{ y \mid y \geq $ $[ \text{Answer Box} ] $ \}
- **D.** The range is the set of all real numbers.

Use integers or fractions as needed for the entries in the boxes.

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