Exercise 6.7.5

Use the notation in Exercise 6.7.2. Then we have

1.

$$T^{\text{†}}(x_1,x_2,x_3)=(\frac{x_1+x_2+x_3}{3},\frac{x_2-x_3}{2}).$$

2.

$$T^{\text{†}}(a+\mathit{bx}+c{x}^2)=a\sqrt{\frac{2}{45}}{f}_3.$$

3.

$$T^{\text{†}}(a+b\sin <!--\; FUNCTION\; APPLICATION\; -->x+c\cos <!--\; FUNCTION\; APPLICATION\; -->x)=\frac{a}{2}+\frac{(2b+c)\sin <!--\; FUNCTION\; APPLICATION\; -->x+(-b+2c)\cos <!--\; FUNCTION\; APPLICATION\; -->x}{5}.$$

4.

$$T^{\text{†}}(z_1,z_2)=\frac{1}{2}(-z_1+(1-i)z_2,(1+i)z_2).$$