Question

Find f + g, f-g, fg, and flg. If f(x) = x - 3 and BIxI= x + 4 4 solution

Answer 1

$$f(x)=x-3, g(x)=x^2+4x$$

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

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

$$(fg)(x)=(x-3)(x^2+4x)=x^3+4x^2-3x^2-12x$$

$$=x^3+x^2-12x$$

$$(\dfrac{f}{g})(x)=\dfrac{x-3}{x^2+4x}=\dfrac{x-3}{x(x+4)}, x\not=0, x\not=-4$$