QUESTION 1
The given functions are;
[tex]f(x)=5x^2-2x[/tex] and [tex]g(x)=5x^2+x-4[/tex]
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=5x^2-2x+3x^2+x-4[/tex]
We regroup like terms to obtain;
[tex](f+g)(x)=5x^2+3x^2-2x+x-4[/tex]
This simplifies to;
[tex](f+g)(x)=8x^2-x-4[/tex]
The correct answer is A.
QUESTION 2
The given functions are;
[tex]f(x)=3x^2+5[/tex] and [tex]g(x)=x-2[/tex].
[tex](fg)(x)=(f(x))(g(x))[/tex]
This implies that;
[tex](fg)(x)=(3x^2+5)(x-2)[/tex]
[tex]\Rightarrow (fg)(x)=3x^3-6x^2+5x-10[/tex]
The correct answer is B.
QUESTION 3
The given functions are
[tex]f(x)=3x^2+10x-8[/tex] and [tex]g(x)=3x^2-2x[/tex].
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
[tex](\frac{f}{g})(x)=\frac{3x^2+10x-8}{3x^2-2x},x\ne0,\frac{2}{3}[/tex]
We factor to obtain;
[tex](\frac{f}{g})(x)=\frac{(x+4)(3x-2)}{x(3x-2)},x\ne0,\frac{2}{3}[/tex]
We cancel the common factors to obtain;
[tex](\frac{f}{g})(x)=\frac{x+4}{x},x\ne0,\frac{2}{3}[/tex]
The correct answer is A.
