1.
[tex](g\times f)(2)[/tex]It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,
[tex]\begin{gathered} (g\times f)(2)=\sqrt[]{11-4x}\times1-x^2 \\ =\sqrt[]{11-4(2)}\times1-(2)^2 \\ =\sqrt[]{3}\times-3 \\ =-3\sqrt[]{3} \end{gathered}[/tex]2.
[tex](g-f)(-1)[/tex]For this we subtract f from g and put -1 into the expression. So
[tex]\begin{gathered} (g-f)(-1)=\sqrt[]{11-4x}-1+x^2 \\ =\sqrt[]{11-4(-1)}-1+(-1)^2 \\ =\sqrt[]{15}-1+1 \\ =\sqrt[]{15} \end{gathered}[/tex]3.
[tex](g+f)(2)[/tex]We simply add f and g and put 2 into the final expression.
[tex]\begin{gathered} (g+f)(2)=\sqrt[]{11-4x}+1-x^2 \\ =\sqrt[]{11-4(2)}+1-(2)^2 \\ =\sqrt[]{3}-3 \end{gathered}[/tex]4.
[tex]\begin{gathered} (\frac{f}{g})(-1) \\ \end{gathered}[/tex]We divide f by g and put -1 in the final expression. Shown below:
[tex]\begin{gathered} (\frac{f}{g})(-1)=\frac{1-x^2}{\sqrt[]{11-4x}} \\ =\frac{1-(-1)^2}{\sqrt[]{11-4(-1)}} \\ =\frac{0}{\sqrt[]{15}} \\ =0 \end{gathered}[/tex]Now, please match each answer with each choice.
