SOLUTION: Find the domain and range of the function: {{{ G(t)=1/(t^2-16) }}} For the domain, I set the denominator equal to 0 and added 16 to both sides. Then, I took the square root of b

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Question 1152172: Find the domain and range of the function:
For the domain, I set the denominator equal to 0 and added 16 to both sides. Then, I took the square root of both sides. This left me with t=4, therefore the domain would be all real numbers except 4. However, this was incorrect... how did I miss the -4 in the domain restriction?
Also, how could I find the range?
Thanks so much!
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!





if =>
if =>

domain:
{ element of : and }

range:
since


......to both sides add -1
-> For a quadratic equation of the form , the discriminant is
For ,,:discriminant is
...expand




it will be for or

{ element of : or }
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the domain and range of the function:
For the domain, I set the denominator equal to 0 and added 16 to both sides. Then, I took the square root of both sides. This left me with t=4, therefore the domain would be all real numbers except 4. However, this was incorrect... how did I miss the -4 in the domain restriction?
Also, how could I find the range?
Thanks so much!
You missed it because when you added 16 to both sides to get: , you should've then taken the SQUARE ROOT of both sides to get: 

Many individuals forget that when the square root is taken of both sides of an equation, the side WITHOUT the square SHOULD include the ± sign. 

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