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

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

Step by step solution

Given information

The function we are given

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

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

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

$(- \infty, - \frac{7}{4}) \cup (- \frac{7}{4}, \infty)$

Conclusion

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

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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

Step by step solution

Given information

We find f+g and its domain

Compute fgand its domain

Conclusion

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Suppose that f(x)=x2-5x+1and g(x)=-4x-7(a) Find f+gand state its domain.(b) Find fgand state its domain.

Short Answer

Step by step solution

Given information

We find f+g and its domain

Compute fgand its domain

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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.