Respuesta :
[tex]\begin{gathered} \text{First of all, we wil find the equations of f and g. Since f is linear, it's slope is:} \\ m=\frac{f(3)-f(2)_{}}{3-2} \\ =\frac{4-6}{1} \\ m=-2 \\ \\ \text{thus, f(x)=-2x+b} \\ \text{now, } \\ f(3)=4, \\ -2(3)+b=4 \\ b=4+6 \\ b=10 \\ \\ f(x)=-2x+10 \\ \\ \\ \text{now we will find g(x)} \end{gathered}[/tex][tex]\begin{gathered} m=\frac{g(1)-g(-1)}{1-(-1)} \\ m=\frac{3-2}{2} \\ m=\frac{1}{2} \\ g(x)=\frac{1}{2}x+b \\ g(1)=3 \\ \frac{1}{2}+b=3 \\ b=3-\frac{1}{2} \\ b=\frac{5}{2} \\ \\ \text{ thus} \\ g(x)=\frac{1}{2}x+\frac{5}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{ Now, since the slopes are not equal, the functions are not parallel.} \\ \text{But, they are opposite reciprocals! because} \\ (-2)(\frac{1}{2})=-1 \\ \text{ thus the functions are perpendicular} \end{gathered}[/tex]
f(x) and g(x) are perpendicular because their slopes are opposite reciprocals!
