Question

Find the domain and range of the function

Answer 1

#2:  This function is not defined if the denominator = 0.  So, steal the denom. and set it = to 0, and then solve the resulting eqn:  3x-1=0, 3x = 1, x = 1/3.
The domain is the set of all real numbers except for x = 1/3.  The range is the set of all real numbers except for y = 0.

#4:  this function will not be defined if 16-x^4 is less than 0.  
so you must solve the inequality x^4 ≤ 16.  Take the 4th root of both sides.  The domain is (-2, 2).  By all means, check.  Suppose x = 1.5.  is x^4≤16? 

The smallest value y can have is zero, which occurs when x = plus or minus 2.