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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q.23 (page 248)

Suppose that $f (x) = x^{2} - 5 x + 1$ and $g (x) = - 4 x - 7$
(a) Find $f + g$ and state its domain.
(b) Find $\frac{f}{g}$ and state its domain.

Short Answer

Expert verified

We have

$a) (f + g) = x^{2} - 9 x - 6 D o m a i n = (- 鈭�, 鈭�) b) \frac{f}{g} = \frac{x^{2} - 5 x + 1}{- 4 x - 7} D o m a i n = (- 鈭�, - \frac{7}{4}) 鈭� (- \frac{7}{4}, 鈭�)$

Step by step solution

01

Given information

The function we are given

$f (x) = x^{2} - 5 x + 1 g (x) = - 4 x - 7$

02

We find f+g and its domain

We get

$(f + g) (x) f (x) + g (x) x^{2} - 5 x + 1 - 4 x - 7 x^{2} - 9 x - 6$

Also the function exist for all real values. Hence the domain of the function is

03

Compute fgand its domain

We have,

$\frac{f}{g} (x) = \frac{f (x)}{g (x)} = \frac{x^{2} - 5 x + 1}{- 4 x - 7}$

Now the function will not exist at $- 4 x - 7 = 0 - 4 x = 7 x = - \frac{7}{4}$

Hence the domain of the function is

$(- 鈭�, - \frac{7}{4}) 鈭� (- \frac{7}{4}, 鈭�)$

04

Conclusion

$a) (f + g) = x^{2} - 9 x - 6 A n d d o m a i n = (- 鈭�, 鈭�) b) \frac{f}{g} = \frac{x^{2} - 5 x + 1}{- 4 x - 7} d o m a i n = (- 鈭�, - \frac{7}{4}) 鈭� (- \frac{7}{4}, 鈭�)$

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