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

Algebra ->  Functions -> 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      Log On


   

Question 1152172: Find the domain and range of the function: +G%28t%29=1%2F%28t%5E2-16%29+
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) About Me  (Show Source):
You can put this solution on YOUR website!

+G%28t%29=1%2F%28t%5E2-16%29+
t%5E2-16+=0
t%5E2-4%5E2=0
%28t-4%29%28t%2B4%29=0
if %28t-4%29=0=>t=4
if %28t%2B4%29=0=>t=-4

domain:
{ t element of R: t%3C%3E-4 and t%3C%3E-4+ }

range:
since +G%28t%29=y
+y=1%2F%28t%5E2-16%29+
+y%28t%5E2-16%29+=1
+yt%5E2-16y+=1......to both sides add -1
+yt%5E2-16y+-1=0-> For a quadratic equation of the form ax%5E2%2Bbx%2Bc=0, the discriminant is b%5E2-4ac
For a=y,b=0,c=-16y-1:discriminant is
0%5E2-4y%28-16y-1%29%3E=0...expand
-4y%28-16y%29-4%28-1%29%3E=0
64y%5E2%2B4%3E=0
16y%5E2%2B1%3E=0

it will be for y%3E0 or y%3C=1%2F16

{ y element of R: y%3C=1%2F16 or y%3E0 }

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain and range of the function: +G%28t%29=1%2F%28t%5E2-16%29+
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: matrix%281%2C3%2C+t%5E2%2C+%22=%22%2C+16%29, 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.