Question

Look at the screenshots for the answers. (50 points)

Answer 1

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Explanation:

Answer 2

(1)

we are given

`f(x)=5x^2-2x`

`g(x)=3x^2+x-4`

`(f+g)(x)=f(x)+g(x)`

now, we can plug

`(f+g)(x)=5x^2-2x+3x^2+x-4`

`(f+g)(x)=8x^2-x-4`...........Answer

(2)

we are given

`f(x)=2x^2-3`

`g(x)=x+4`

`(fg)(x)=f(x) * g(x)`

now, we can plug

`(fg)(x)=(2x^2-3) * (x+4)`

`(fg)(x)=2x^3+8x^2-3x-12`...........Answer

(3)

we are given

`f(x)=3x^2+10x-8`

`g(x)=3x^2-2x`

we have

`((f)/(g) )(x)=(f(x))/(g(x))`

now, we can plug values

`((f)/(g) )(x)=(3x^2+10x-8)/(3x^2 -2x)`

now, we can factor it

`((f)/(g) )(x)=((3x-2)(x+4))/(x(3x -2))`

now, we can factor it

`((f)/(g) )(x)=((x+4))/(x)`

we know that denominator can not be zero

so,

`3x^2-2x\\eq 0`

`x\\eq 0, x\\eq (2/3)`

so, option-C.........Answer

(4)

we are given

`r(x)=x^2+6x+10`

`c(x)=x^2-4x+5`

`(r-c)(x)=r(x)-c(x)`

now, we can plug it

`(r-c)(x)=x^2+6x+10-(x^2-4x+5)`

`(r-c)(x)=10x+5`

now, we can plug x=4

`(r-c)(4)=10*4+5`

`(r-c)(4)=45`

so, option-C..................Answer

(5)

we are given

`c(x)=50+5x`

`p(x)=100-2x`

`(p*c)(x)=p(x)*c(x)`

now, we can plug values

`(p*c)(x)=(50+5x)*(100-2x)`

now, we can plug x=2

`(p*c)(2)=(50+5*2)*(100-2*2)`

`(p*c)(2)=5760`

we know that

price is

`c(x)=50+5x`

we can plug x=2

`c(2)=50+5*2`

`c(2)=60`

so, option-B...............Answer