Answer:
Step-by-step explanation:
f(x) = 1 - x²
g(x) = [tex]\sqrt{11-4x}[/tex]
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
[tex](\frac{f}{g})(x)=\frac{1-x^2}{\sqrt{11-4x}}[/tex]
[tex](\frac{f}{g})(-1)=\frac{1-(-1)^2}{\sqrt{11-4(-1)}}[/tex]
= [tex]\frac{1-1}{\sqrt{15}}[/tex]
= 0
(g + f)(x) = g(x) + f(x)
= [tex]\sqrt{11-4x}+1-x^2[/tex]
(g + f)(2) = [tex]\sqrt{11-4(2)}+1-(2)^2[/tex]
= [tex]\sqrt{3}-3[/tex]
(g - f)(x) = g(x) - f(x)
= [tex]\sqrt{11-4x}-(1-x^2)[/tex]
= [tex]\sqrt{11-4x}-1+x^2[/tex]
(g - f)(-1) = [tex]\sqrt{11-4(-1)}-1+(-1)^2[/tex]
= [tex]\sqrt{15}[/tex]
(g . f)(x) = g(x) × f(x)
= [tex](\sqrt{11-4x})(1-x^2)[/tex]
(g . f)(2) = [tex](\sqrt{11-4(2)})(1-(2)^2)[/tex]
= [tex]\sqrt{3}(-3)[/tex]
= -3√3
