##### Consider the following functions. f(x) = 36 − x2 , g(x) = 1 + x Find (f +

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Consider the following functions.

f(x) =
 36 − x2
,   g(x) =
 1 + x
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).

Jun 30th, 2015

we have f(x) = 36 - x² and g(x) = 1 + x

so :

1) - (f + g)(x) = (36 - x²) + (1 + x) = -x² + x + 37

and the domain is :  D(f+g) =  IR = ]-infini , 0]U[0, +infini[

2) -  (f - g)(x) = (36 - x²) - (1 + x) = - x² - x + 35

and the domain is : D(f - g) = IR =  ]-infini , 0]U[0, +infini[

3) - (fg)(x) = (36 - x²) * (1 + x)  = 36 + 36x - x² - x^3 = - x^3  - x²  + 36x + 36

and the domain is :  D(fg) = IR =  ]-infini , 0 ] U [ 0, +infini[

4) - (f/g)(x) = (36 - x²) / (1 + x) =  (- x² + 36) / ( x + 1)

and the domain is : D(f/g) = {x c IR /  x + 1 =/= 0 }

so : D(f/g) = {x c IR /  x =/= -1 }

so :  D(f/g) = ]- infini , -1 ] U [-1 , + infini [

if you dont understand something just ask ,

and

Please Each time you have any others homework invite me first i will give you the best answers

Good Luck

Jun 30th, 2015

we have f(x) = 36 - x² and g(x) = 1 + x

so :

1) - (f + g)(x) = (36 - x²) + (1 + x) = -x² + x + 37

and the domain is :  D(f+g) =  IR = ]-infinity , 0]U[0, +infinity[

_____________________________________________

2) -  (f - g)(x) = (36 - x²) - (1 + x) = - x² - x + 35

and the domain is : D(f - g) = IR =  ]-infinity , 0]U[0, +infinity[

_____________________________________________

3) - (fg)(x) = (36 - x²) * (1 + x)  = 36 + 36x - x² - x^3 = - x^3  - x²  + 36x + 36

and the domain is :  D(fg) = IR =  ]-infinity , 0 ] U [ 0, +infinity[

_____________________________________________

4) - (f/g)(x) = (36 - x²) / (1 + x) =  (- x² + 36) / ( x + 1)

and the domain is : D(f/g) = {x c IR /  x + 1 =/= 0 }

so : D(f/g) = {x c IR /  x =/= -1 }

so :  D(f/g) = ]- infinity , -1 ] U [-1 , + infinity [

_______________________________________________

if you dont understand something just ask ,

and

Please Each time you have any others homework invite me first i will give you the best answers

Good Luck

Jun 30th, 2015

sqrt 36

Jun 30th, 2015

What you mean with sqrt (36)  ???

Jun 30th, 2015

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Jun 30th, 2015
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Jun 30th, 2015
Sep 24th, 2017
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