Q 28. Find the domain of the composite... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 28. (page 257)

Find the domain of the composite function $f 鈭� g$ .
$f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$

Short Answer

Expert verified

Domain of the composite function $f 鈭� g$ of $f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$ is $[2, 鈭�)$ .

Step by step solution

Step 1. Given information.

We have given,

$f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$

Step 2. Concept used.

Domain is the set of all input values where the function is well defined and real.

Step 3. Explanation.

We have,

$f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$

Here we have g(x) is radical function and the function g(x) is well defined and real for all values of x grater than equal to 2.

That is,

$[2, 鈭�)$

Similarly domain of the function f(x) is polynomial function and domain of the polynomial function is set of all real numbers.

That is,

$(- 鈭�, 鈭�)$

Therefore domain of the composite function of $f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$ is the intersection of the domain of f(x) and domain of g(x).

So domain of composite function of $f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$ is

$[2, 鈭�) .$

Step 4. Conclusion.

Hence, domain of the composite function $f 鈭� g$ of $f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2} i s [2, 鈭�)$ .

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91影视

Find the domain of the composite function $f 鈭� g$ .
$f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

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91影视

Find the domain of the composite function f鈭�g.f(x)=x2+4andg(x)=x-2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Find the domain of the composite function $f 鈭� g$ .
$f (x) = x^{2} + 4 a n d g (x) = \sqrt{x - 2}$