Question

Find the domain and range (with steps )

$f(x) = \frac{x}{ {x}^{2} + 2}$
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Answer 1

Question :-

Find the domain and range (with steps )

$f(x) = \frac{x}{ {x}^{2} + 2}$

Answer:-

Explanation :-

We have,

$f(x) = \frac{x}{ {x}^{2} + 2} \\ let \: \\ \\ \implies \: y \: = \frac{x}{ {x}^{2} + 2 }$

Now find the value of" x" in terms of" y",

$\implies \: y \: {x}^{2} + 2y = x \\ \\ \implies \: y \: {x}^{2} - x + 2y = 0 \\ \\ solve \: this \: equation \: \\ \\ \implies \: y \: {x}^{2} - x = - 2y \\ \\ \implies \: x(xy - 1) = - 2y \\ \\ case \: (1) \\ \\ \implies \: x = - 2y \\ \\ exchange \: x \: to \: y \: and \: y \: to \: x \\ \\ \implies \: y = - 2x \\ \\ case \: (2) \\ \\ \implies \: xy - 1 = - 2y \\ \\ \implies \: xy = 1 - 2y \\ \\ \implies \: x = \frac{1 - 2y}{y} \\ \\ again \: exchange \: \\ \\ \implies \: y = \frac{1 - 2x}{x}$

Here ,x≠0

x € R ( any real number ),