Chapter 10: Q88. (page 530)

Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = x + 3 and g (x) = x^{2}$ .

Short Answer

Expert verified

The value of $g [h (x)] = x^{2} + 6 x + 9 and h [g (x)] = x^{2} + 3$ .

Step by step solution

Step 1. Write down the given equation.

The given functions are $h (x) = x + 3 and g (x) = x^{2}$ .

Step 2. Evaluating ghx and hgx.

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

$\begin{matrix} g (x) = x^{2} .... (Given) \\ g [h (x)] = {[h (x)]}^{2} .... (Plugging x = h (x)) \\ g [h (x)] = {(x + 3)}^{2} .... (∵ h (x) = x + 3) \\ g [h (x)] = x^{2} + 6 x + 9 \\ Now, h (x) = x + 3.... (Given) \\ h [g (x)] = [g (x)] + 3.... (Plugging x = g (x)) \\ h [g (x)] = (x^{2}) + 3.... (∵ g (x) = x^{2}) \\ h [g (x)] = x^{2} + 3 \end{matrix}$

Step 3. Conclusion.

The value of $g [h (x)] = x^{2} + 6 x + 9 and h [g (x)] = x^{2} + 3$

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Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = x + 3 and g (x) = x^{2}$ .

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Evaluating ghx and hgx.

Step 3. Conclusion.

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Find ghx andhgxfor the functions hx=x+3andgx=x2.

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

Pure Maths

Geometry

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find $g [h (x)] and h [g (x)]$ for the functions $h (x) = x + 3 and g (x) = x^{2}$ .