Calculus, 8th Edition,stewart; page 44 problem 31

Question

Find (a) f + g, (b) f - g, (c) fg, and (d) f/g and state their domains.

f (x) = x^3 + 2x^2,     g(x) = 3x^2 - 1

Answer 1

Step:1

The functions are  and .

:

All possible values of  is the domain of the function.

The domain of  is the set all real numbers.

 :

All possible values of  is the domain of the function.

The domain of  is the set all real numbers.

(a)

Find .

 

.

All possible values of  is the domain of the function.

So the domain of  is the set all real numbers.

The domain of  is .

Step:2

(b)

Find .

 

.

All possible values of  is the domain of the function.

So the domain of  is the set all real numbers.

The domain of  is .

Step:3

(c)

Find .

 

.

All possible values of  is the domain of the function.

So the domain of  is the set all real numbers.

The domain of  is .

Step:4

(d)

Find .

 

.

All possible values of  is the domain of the function.

But denominator of the function should not be a zero.

The domain of  is .

Solution:

(a) , and its domain is .

(b) , and its domain is .

(c) , and its domain is .

(d) , and its domain is .