Question #119437
Let f : R2-->R1be defined by
f(x1, x2) = (3x1+ 4x2)and T : R2--> R2be
defined by T(x1 , x2) = (x1- x2, x1+ x2).
Suppose g = f o T. What is g (2, 3) ?
1
Expert's answer
2020-06-01T19:19:09-0400

f(x1,x2)=3x1+4x2T(x1,x2)=(x1x2,x1+x2)g(x1,x2)=f(x1,x2)T(x1,x2)==3(x1x2)+4(x1+x2)=7x1+x2g(2,3)=72+3=17f(x_1,x_2)=3x_1+4x_2\\ T(x_1,x_2)=(x_1-x_2,x_1+x_2)\\ g(x_1,x_2)=f(x_1,x_2)\circ T(x_1,x_2)=\\ =3(x_1-x_2)+4(x_1+x_2)=7x_1+x_2\\ g(2,3)=7\cdot2+3=17


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