SOLUTION: Find the Domain and Range of the function: 1/x^4.

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Question 62555This question is from textbook
: Find the Domain and Range of the function: 1/x^4. This question is from textbook

Found 2 solutions by uma, Edwin McCravy:
Answer by uma(370) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = 1/x^4
Here we find that the function is undefined when x takes the value 0.
Which means that x can take any real value other than zero
So domain = R - {0}
We find that for any value of x, x^4 is always positive.
So range of the function = the set of positive real numbers
That is Range = R+

Good Luck!!!

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the Domain and Range of the function: 1/x4.

There are only two things which restrict the domain 
or range of a function in ordinary algebra.

1.  Denominators which must never be 0.
2.  Even root radicands which must never be negative.

If there are no denominators or even root radicands 
which contain variables then the domain is always
(-¥, ¥)

             1
y = f(x) = ----
            x4

has a denominator with a variable, so we must 
require that x4 ¹ 0, or x ¹ 0

So the domain is 

      (-¥, 0) È (0, ¥)

To find the range, we solve the equation for x, 
and use the same criteria for y.

             1
       y = ----
            x4

Multiply both sides by x4

     x4y = 1

            1 
      x4 = ---
            y

             1
      x =  -----
            4Öy

This is an even root radical, therefore its radicand, y
must not be negative. Since it is also in a denominator
it must not be 0 either.  Therefore it must by greater
than 0, or y > 0.  Therefore the range is

       (0, ¥)

Edwin