Math, asked by YashasviThwal, 1 month ago

the domain of f(x) = x^2/x^2 + 3​

Answers

Answered by senboni123456
0

Step-by-step explanation:

Let

y =  \frac{ {x}^{2} }{ {x}^{2}  + 3}  \\

 \implies \: y ( {x}^{2}  + 3)=   {x}^{2}  \\

 \implies \: y  {x}^{2}  + 3y=   {x}^{2}  \\

 \implies \: y  {x}^{2}  -  {x}^{2}  + 3y=   0  \\

 \implies \: (y  - 1) {x}^{2}   + 3y=   0  \\

 \implies \:  {x}^{2}   =   \frac{3y}{1 - y}  \\

 \implies \:  x   =    \sqrt{\frac{3y}{1 - y} } \\

Now,

 \implies \:      \frac{3y}{1 - y}  \geqslant 0 \\

 \implies \:      \frac{y}{1 - y}  \geqslant 0 \\

 \implies \:      \frac{y}{ y - 1}  \leqslant 0 \\

 \implies\: y\in[0,1)

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