If $f (x) = x^{2} + 1$ and $g (x) = 2 x$ , then find the domain of the function
$h (x) = \frac{(f + g) x}{(f - g) x}$

(- \infty, \infty) - {- 1}

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(- \infty, \infty) - {1}

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(- \infty, - 1) \cup (0, \infty)

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(- \infty, \infty)

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Solution

The correct option is B $(- \infty, \infty) - {1}$
$\frac{(f + g) x}{(f - g) x} = \frac{(f (x) + g (x))}{(f (x) - g (x))}$
$= \frac{x^{2} + 1 + 2 x}{x^{2} + 1 - 2 x} = \frac{{(x + 1)}^{2}}{{(x - 1)}^{2}}$
$∵$ x can take all values except 1 since the denominator cannot be equal to zero.
Therefore, the domain of the given function is $(- \infty, \infty) - {1}$

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