Determine If the Given Function Can Be Extended to a Continuous

Multiple Choice

Determine if the given function can be extended to a continuous function at x = 0. If so, approximate the extended
function's value at x = 0 (rounded to four decimal places if necessary) . If not, determine whether the function can be
continuously extended from the left or from the right and provide the values of the extended functions at x = 0.
Otherwise write "no continuous extension."
- $$f ( x ) = ( 1 + 2 x ) ^ { 1 / x }$$

A) f(0) = 7.3891
B) No continuous extension
C) f(0) = 5.4366
D) f(0) = 2.7183