frustrating domains and range!!!!!!!

[mousey12354]

Hey
so im having problems with finding the domain and range of

y1(x)= 1/ sqrt 9 - x ^2

and

y2(x)= x3+x/ x-2

i think its the square root in the first one thats throwing me off... does that mean x< 9??

any help would be much appreciated!!!!

 

[lookagain]

Hey
so im having problems with finding the domain and range of

y1(x)= 1/ sqrt 9 - x ^2

and

y2(x)= x3+x/ x-2

i think its the square root in the first one thats throwing me off... does that mean x< 9??

any help would be much appreciated!!!!

mousey12354,

you place grouping symbols around the appropriate parts of the fractions, etc., as they
are needed, because of the Order of Operations.


Did you mean:


\(\displaystyle y_1(x) \ = \ 1/(\sqrt{9 - x^2}) \ = \ \dfrac{1}{\sqrt{9 - x^2}} \ \ and\)


\(\displaystyle y_2(x) \ = \ (x^3 + x)/(x - 2) \ = \ \dfrac{x^3 + x}{x - 2} \ ?\)


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So the radicand must be strictly positive because the square root of it is in the denominator.


\(\displaystyle Solve: \ \ 9 - x^2 \ > \ 0\)


\(\displaystyle -1(9 - x^2) \ < \ -1(0)\)


\(\displaystyle -9 + x^2 < 0\)


\(\displaystyle x^2 - 9 < 0\)


\(\displaystyle x^2 < 9\)


Can you solve this inequality?