Answer:
(f+g)(x)=5x²-4x+3
(f-g)(x)=3x²-2x+3
(fg)(x)[tex]=4x^4-7x^3+15x^2-9x[/tex]
[tex]\frac{f}{g}(x)[/tex] [tex]=\frac{4x^2-3x}{x^2-x+3}[/tex]
Step-by-step explanation:
Given that,
f(x)=4x²-3x
g(x)=x²-x+3
(f+g)(x)
=f(x)+g(x)
=4x²-3x+x²-x+3
=(4x²+x²)+(-3x-x)+3 [ combined the like terms]
=5x²-4x+3
(f-g)(x)
=f(x)-g(x)
=4x²-3x-(x²-x+3)
=4x²-3x-x²+x-3
=(4x²-x²)+(-3x+x)-3 [ combined the like terms]
=3x²-2x+3
(fg)(x)
=f(x).g(x)
=(4x²-3x).(x²-x+3)
=4x²(x²-x+3)-3x(x²-x+3)
[tex]=4x^4-4x^3+12x^2-3x^3+3x^2-9x[/tex]
[tex]=4x^4+(-4x^3-3x^3)+(12x^2+3x^2)-9x[/tex]
[tex]=4x^4-7x^3+15x^2-9x[/tex]
[tex]\frac{f}{g}(x)[/tex]
[tex]=\frac{f(x)}{g(x)}[/tex]
[tex]=\frac{4x^2-3x}{x^2-x+3}[/tex]
