Consider the function f: epsilon rightarrow epsilon defined by f(x, y) = (-y, x

Question

Consider the function f: epsilon rightarrow epsilon defined by f(x, y) = (-y, x + y^2) for all (x, y) elementof epsilon, (a). Prove that f is a transformation and find a formula for f^-1 (x, y) (b). Show that f is not isometry (c). Find all fixed points of f. (d). Describe the images of straight lines under the transformation f. Find the expression of the lines which one mapped either to a line or parabola (e). Find the equation of f(l) and f(m), where L is the line with equation y = 5 and m is the line with equation x = 0

Explanation / Answer

a)f(x,y)+f(z,w)=f(x+z,y+w)=(-y-w,x3+y3+y2+w2)

=f(x+z,y+w)

hence it is a linear transformation.

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