Chapter 10: Q87. (page 530)

Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = 2 x - 1 and g (x) = x - 5$ .

Short Answer

Expert verified

The value of $g [h (x)] = 2 x - 6 and h [g (x)] = 2 x - 11$ .

Step by step solution

Step 1. Write down the given equation.

The given functions are $h (x) = 2 x - 1 and g (x) = x - 5$ .

Step 2. Evaluating ghx and hgx.

The value of $g [h (x)] and h [g (x)]$ is evaluated as:

$\begin{matrix} g (x) = x - 5.... (Given) \\ g [h (x)] = [h (x)] - 5.... (∵ h (x) = 2 x - 1) \\ g [h (x)] = (2 x - 1) - 5 \\ g [h (x)] = 2 x - 6 \\ Now, h (x) = 2 x - 1.... (Given) \\ h [g (x)] = 2 [g (x)] - 1.... (∵ g (x) = x - 5) \\ h [g (x)] = 2 (x - 5) - 1 \\ h [g (x)] = 2 x - 11 \end{matrix}$

Step 3. Conclusion.

The value of $g [h (x)] = 2 x - 6 and h [g (x)] = 2 x - 11$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = 2 x - 1 and g (x) = x - 5$ .

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Evaluating ghx and hgx.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find ghx andhgxfor the functions hx=2x-1 andgx=x-5.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Evaluating ghx and hgx.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = 2 x - 1 and g (x) = x - 5$ .