Answer:
(g-f) (-1)= [tex]\sqrt{15}[/tex]
(f/g)(-1)= 0
(g+f)(2) = [tex]\sqrt{3}-3[/tex]
(g*f)(2) = [tex]-3 \sqrt{3}[/tex]
Step-by-step explanation:
Given :
[tex]f(x)=1-x^2\\g(x)=\sqrt{11-4x}[/tex]
To find : [tex](g-f)(-1)[/tex]
Solution :
[tex]g(x)-f(x)=\sqrt{11-4x}-1+x^2\\(g-f)(x)=\sqrt{11-4x}-1+x^2\\(g-f)(-1)=\sqrt{11+4}-1+1=\sqrt{15}[/tex]
To find : [tex]\left ( \frac{f}{g} \right )(-1)[/tex]
Solution :
[tex]\frac{f(x)}{g(x)}=\frac{1-x^2}{\sqrt{11-4x}}\\\frac{f(-1)}{g(-1)}=\frac{1-1}{\sqrt{11+4}}=0[/tex]
To find :[tex](g+f)(2)[/tex]
Solution:
[tex]g(x)+f(x)=\sqrt{11-4x}+1-x^2\\(g+f)(x)=\sqrt{11-4x}+1-x^2\\(g+f)(2)=\sqrt{11-8}+1-4=\sqrt{3}-3[/tex]
To find: [tex](g\times f)(2)[/tex]
Solution:
[tex]g(x)f(x)=(gf)(x)=\sqrt{11-4x}(1-x^2)\\(gf)(2)=\sqrt{11-8}(1-4)=-3\sqrt{3}[/tex]
