Question 1032654
f(2) = 1 ==> {{{a*2^r = 1}}} <-------Equation A

while 

f(32) = 4 ==> {{{a*32^r = 4}}}.  <------Equation B.

Divide Equation B by corresponding sides of equation A:

==> {{{16^r = 4}}}

==> r = 1/2.

BTW, {{{a = 1/sqrt(2)}}}, and the function is {{{f(x) = sqrt(x/2)}}}