**Title: Sum, Difference, and Product of Two Functions****Overview:**Suppose that the functions \( s \) and \( t \) are defined for all real numbers \( x \) as follows:\[ s(x) = x + 3 \]\[ t(x) = 4x - 6 \]**Task:**Write the expressions for \( (t+s)(x) \) and \( (t-s)(x) \) and evaluate \( (t \cdot s)(1) \).**Expressions:**1. \( (t+s)(x) = \) [Enter your answer here]2. \( (t-s)(x) = \) [Enter your answer here]3. \( (t \cdot s)(1) = \) [Enter your answer here]**Note:**To solve these problems, use the following operations:- Addition: \( (t+s)(x) = t(x) + s(x) \)- Subtraction: \( (t-s)(x) = t(x) - s(x) \)- Multiplication: \( (t \cdot s)(1) = t(1) \cdot s(1) \)Once you have entered your answers, click "Check" to see if they are correct.**Additional Features:**- The interface includes options for further Explanation and a Check button to validate your inputs.

Topic = Functionss(x)=x+3t(x)=4x-61) t+sx=tx+sx⇒4x-6+x+3=5x-32) t-sx=tx-sx⇒4x-6-x-3=3x-93)t.sx=tx.sx=4x-6×x+3 = 4x2+6x-18put x=1t.s1= 412+61-18=-8

Math

Algebra

Suppose that the functions s and t are defined for all real numbers x as follows. s (x)=x+3 t(x)=4x-6 Write the expressions for (t+s)(x) and (t-s)(x) and evaluate (t's)(1). (++)(+) = [0 %3D (1-)(*) = D %3D (rs)(1) = 1 %3D

Suppose that the functions s and t are defined for all real numbers x as follows. s (x)=x+3 t(x)=4x-6 Write the expressions for (t+s)(x) and (t-s)(x) and evaluate (t's)(1). (++)(+) = [0 %3D (1-)(*) = D %3D (rs)(1) = 1 %3D

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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Question

**Title: Sum, Difference, and Product of Two Functions**

**Overview:**

Suppose that the functions \( s \) and \( t \) are defined for all real numbers \( x \) as follows:

\[ s(x) = x + 3 \]

\[ t(x) = 4x - 6 \]

**Task:**

Write the expressions for \( (t+s)(x) \) and \( (t-s)(x) \) and evaluate \( (t \cdot s)(1) \).

**Expressions:**

1. \( (t+s)(x) = \) [Enter your answer here]

2. \( (t-s)(x) = \) [Enter your answer here]

3. \( (t \cdot s)(1) = \) [Enter your answer here]

**Note:**

To solve these problems, use the following operations:

- Addition: \( (t+s)(x) = t(x) + s(x) \)
- Subtraction: \( (t-s)(x) = t(x) - s(x) \)
- Multiplication: \( (t \cdot s)(1) = t(1) \cdot s(1) \)

Once you have entered your answers, click "Check" to see if they are correct.

**Additional Features:**

- The interface includes options for further Explanation and a Check button to validate your inputs.

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