Question

For each pair of functions give a characteristic that the two functions have in common and a characteristic that distinguishes them.

a) f(x)=1/x and g(x)=sinx

b) f(x)=x and g(x)=[x]

c) f(x)=2^x and g(x)=sinx

Answer 1

a) they are odd
but 1/x is undefined at x = 0

b) linear
but x is odd and |x| is even

c) d/dx (2^x) = 2^x ln 2 so both derivatives keep repeating

but sin x is periodic