Needed help with this math question.

Question

Use f(x) = x+3 and g(x) = f+8 to find each of the following

(a) (f+g) (x)=?

(b) (f-g) (x)=?

(c) (fg) (x) =?

(d) (f/g) (x)=?

Answer 1

f(x) = x + 3 , g(x) = f(x) + 8
If f(x) = x + 3 then g(x) = (x + 3) + 8 = x + 11
(a). (f + g)(x) = (x + 3) + (x + 11) = 2x + 14
(b). (f - g)(x) = (x + 3) - (x + 11) = - 8 
(c). (f*g)(x) = (x + 3)(x + 11) = x(x + 11) + 3(x + 11) = x² + 14x + 33 
(d). (f/g)(x) = (x + 3) / (x + 11)

Answer 2

In order to make this easier I tried to put f(x) in bold and orange, and g(x) and green in italics. 

Here is an example so that you can do this problem:

f(x)= 3x+2     g(x)=f+3

(a) (f+g)(x)=f(x)+g(x)=3x+2+f+3 = 3x+f+5= 3x+3x+2+5=6x+7    

(b) (f-g)(x)=f(x)-g(x)=(3x+2)-(f+3) = 3x+2-f-3=3x-f-1=3x-(3x+2)-1=3x-3x-2-1=-3  

 (Hint: Remember that it is minus all of g(x))

(c) (fg)(x)=f(x)g(x)=(3x+2)(f+3) = 3xf+9x+2f+6=3x(3x+2)+9x+2(3x+2)+6

=9x²+6x+9x+6x+4+6=9x² +21x+10 

OR (3x+2)(f+3)=(3x+2)(3x+2+3)=(3x+2)(3x+5)=9x²+6x+15x+10

=9x2 +21x+10 

(Hint: Remember to use FOIL and the distributive property)

(d) (f/g)(x)=f(x)/g(x)=(3x+2)/(f+3)=(3x+2)/(3x+2+3)=(3x+2)/(3x+5)     

(Hint: We cannot simplify any more!)

 

Hint: To make this even easier you could just make g(x)=3x+2+3= 3x+5 then plug this in for g(x). I did this for you in the OR part (c).