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Step-by-step explanation:

f(x) = 6x³-x²+4x+5

g(x) = 9x³-1

(f+g)(x) = {6x³-x²+4x+5} + {9x³-1}

open brackets

6x³-x²+4x+5 + 9x³-1

choose like terms

6x³+ 9x³-x²+4x+5 -1

15x³-x²+4x+4= x²(15x-1)+4(x+1)= (x²+4)(x+1)(15x-1)

(f+g)(x)= 15x³-x²+4x+4 =  (x²+4)(x+1)(15x-1)

(f+g)(2) = 15(2)³-(2)²+4(2)+4 = 15(8)-4+8+4 = 120+8 = 128

(f-g)(x) = {6x³-x²+4x+5} - {9x³-1}

open brackets

6x³-x²+4x+5 - 9x³+1

choose like terms

6x³- 9x³-x²+4x+5 +1

-3x³-x²+4x+6= -x²(3x+1)+2(2x+3)= (-x²+2)(3x+1)(2x+3) =  (2-x²)(3x+1)(2x+3)

(f-g)(x) = -3x³-x²+4x+6 = (2-x²)(3x+1)(2x+3)

(f-g)(-3) = -3(-3)³-(-3)²+4(-3)+6 = -3(-3x-3x-3)-(-3x-3)-12+6=-3(-27)-3(9)-12+6= 81-27-12+6 = 54-6= 48

(f-g)(-3) = 48

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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step-by-step explanation: