Consider the following functions.

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f(x) = x2 + 5x,      g(x) = 7x2 − 1

Find 

(f + g)(x)

 Find the domain of (f + g)(x).

Find (f − g)(x).

Find the domain of (f − g)(x)

Find (fg)(x).

Find the domain of (fg)(x)

Find 

f
g
(x).

 

 Find the domain of 

f
g
(x).

 

Feb 23rd, 2015

we have the subsequent conclusions:

(f+g)(x)= 8x^2 + 5x -1

the domain of f+g is the set of all real numbers, since it is a polynomial function and then it is an integer function

(f-g)(x)= - 6x^2 + 5x +1

here the domain of f-g is the set of all real numbers, since it is a polynomial (integer) function.

(f*g) (x) = 7x^4 +35 x^3 - x^2 - 5x

again f*g is a polynomial (integer) function so its domain is the set of real numbers

(f/g) (x) = (x^2+5x)/ (7*(x^2-1/7))

here that function is not defined in x= 1/sqrt(7) and x= -1/sqrt(7), so itsdomain is:

(-infinity, -1/sqrt(7)) union (-1/sqrt(7), 1/sqrt(7)) union (1/sqrt(7), +infinity)

Feb 23rd, 2015

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Feb 23rd, 2015
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Feb 23rd, 2015
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