(1)
we are given
[tex]f(x)=5x^2-2x[/tex]
[tex]g(x)=3x^2+x-4[/tex]
[tex](f+g)(x)=f(x)+g(x)[/tex]
now, we can plug
[tex](f+g)(x)=5x^2-2x+3x^2+x-4[/tex]
[tex](f+g)(x)=8x^2-x-4[/tex]...........Answer
(2)
we are given
[tex]f(x)=2x^2-3[/tex]
[tex]g(x)=x+4[/tex]
[tex](fg)(x)=f(x) \times g(x)[/tex]
now, we can plug
[tex](fg)(x)=(2x^2-3) \times (x+4) [/tex]
[tex](fg)(x)=2x^3+8x^2-3x-12[/tex]...........Answer
(3)
we are given
[tex]f(x)=3x^2+10x-8[/tex]
[tex]g(x)=3x^2-2x[/tex]
we have
[tex](\frac{f}{g} )(x)=\frac{f(x)}{g(x)}[/tex]
now, we can plug values
[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2 -2x}[/tex]
now, we can factor it
[tex](\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x -2)}[/tex]
now, we can factor it
[tex](\frac{f}{g} )(x)=\frac{(x+4)}{x}[/tex]
we know that denominator can not be zero
so,
[tex]3x^2-2x\neq 0[/tex]
[tex]x\neq 0, x\neq (2/3)[/tex]
so, option-C.........Answer
(4)
we are given
[tex]r(x)=x^2+6x+10[/tex]
[tex]c(x)=x^2-4x+5[/tex]
[tex](r-c)(x)=r(x)-c(x)[/tex]
now, we can plug it
[tex](r-c)(x)=x^2+6x+10-(x^2-4x+5)[/tex]
[tex](r-c)(x)=10x+5[/tex]
now, we can plug x=4
[tex](r-c)(4)=10*4+5[/tex]
[tex](r-c)(4)=45[/tex]
so, option-C..................Answer
(5)
we are given
[tex]c(x)=50+5x[/tex]
[tex]p(x)=100-2x[/tex]
[tex](p*c)(x)=p(x)*c(x)[/tex]
now, we can plug values
[tex](p*c)(x)=(50+5x)*(100-2x)[/tex]
now, we can plug x=2
[tex](p*c)(2)=(50+5*2)*(100-2*2)[/tex]
[tex](p*c)(2)=5760[/tex]
we know that
price is
[tex]c(x)=50+5x[/tex]
we can plug x=2
[tex]c(2)=50+5*2[/tex]
[tex]c(2)=60[/tex]
so, option-B...............Answer
