Find the domain of f?

Question

Let f be given by the formula:

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Answer 1 · 2018-03-01T12:02:53

$(- \infty, - 3) \cup (1, \infty)$ $(-oo,-3)uu(1,oo)$

The domain is defined as all possible values of $x$ $x$ for which $f (x)$ $f(x)$ will be defined.

Here, as $x^{2} + 2 x - 3 \to 0$ $x^2+2x-3rarr0$ , $f (x) \to \pm \infty$ $f(x)rarr+-oo$ .

We can say that $f (x)$ $f(x)$ is undefined when $x^{2} + 2 x - 3 = 0$ $x^2+2x-3=0$ . Solving for $x$ $x$ :

$x^{2} + 2 x - 3 = 0$ $x^2+2x-3=0$

$x^{2} + 3 x - x - 3 = 0$ $x^2+3x-x-3=0$

$x (x + 3) - 1 (x + 3) = 0$ $x(x+3)-1(x+3)=0$

$(x + 3) (x - 1) = 0$ $(x+3)(x-1)=0$

So $f (x)$ $f(x)$ is undefined when $x = 1$ $x=1$ and $x = - 3$ $x=-3$ .

In interval notation, we can write this as:

$(- \infty, - 3) \cup (1, \infty)$ $(-oo,-3)uu(1,oo)$