Find the image of the point (3,0) under the mapping Ho degree T-2,0 degree Ry=x."?

Answer 1

Your notation is not standard so I will have to make an educated guess here. CHECK IF YOUR SOURCE USES THE SYMBOLS IN THIS MEANING!

I assume that you mean the composition of the three transformations

H0 : horizontal reflection around y-axis
T(-2,0) : translation over vector (-2,0)
R(y=x) : reflection in the line y = x

The "degree" symbols (actually called "composition") indicate that these transformations must be applied from right to left.

First, reflection in the line y=x involves swapping the x- and y-coordinates.
Then, translating over (-2,0) means that we must add -2 to x and 0 to y.
Finally, reflection in the y-axis means changing the sign of the x-coordinate.

So we have
(3, 0) --> (0, 3) --> (-2, 3) --> (2,3)

The last point is the answer.