Question

Is it possible to perform two reflections of an object so that the final image is identical to the original image? If so, give an example. If not , explain your reasoning

Answer 1

Yes, it is possible

Explanation:

Take a function y= f(x). When it is reflected across the x-axis the x-coordinates do not change but the y coordinates become the negative of the pre-image

In other words reflection f'(x) of f(x) over the x-axis is y = -f(x)

If we reflect f'(x) over the x-axis then the resultant reflection is

f''(x) = -f'(x) = -(-f(x)) = f(x)

So we get the original image after two consecutive reflections along the x-axis