Question

given f(x)=3x^2+5x+2 and g(x)+x-1:
a)find (f+g)(x)
b)find (fg)(x)
c)find (f*g)(x)

Answer 1

c) is an open circle between f and g dont know what its called

Answer 2

I am assuming g(x)=x-1
a)(f+g)(x) simply means f(x)+g(x)
so we find just add the two functions,
(3x^2+5x+2) + (x-1)
which gives
(3x^2+6x+1)

Answer 3

b)(fg)(x) means that the two functions are multiplied, this means f(x)*g(x)
this gives
(3x^2+5x+2)(x-1)
=(3x^3+2x^2-3x-2)
c)open circle that is, (f o g)(x) means,
f(g(x)).
this means that wherever there is x in the function f, we replace it with the value of g(x).that means, in the function f, we replace x with x-1
so now we get,
f(x-1).so this is
3(x-1)^2+5(x-1)+2
= 3(x^2 -2x +1)-5(x-1)+2
=3x^2-11x+10

Answer 4

thankyou really appriciate it