Assume your friend just sent you 32 bits of pixel data (just the 0s and 1s for black and white pixels). could you recover the original image? if so, how? if not, why not?

No , we cannot recover the original image.

Because the image is 2d array of pixels and each pixel contains r,g,b values but in current scenario we have only 1 and 0 from which we cannot recover the (r,g,b) of the pixel so we cannot recover the original image.

answer; i believe that the correct answer is (b) slow down to 5 mph

to answer your question:

f(x)= a^x.  if x=0, f(x)=1  if x=1, f(x)=a  if x=1, f(x)=a^a