Hw do you find the domain for $f (x) = \frac{2 x + 7}{x^{2} - 13 x - 30}$ $f(x)= (2x+7)/(x^2-13x-30)$ ?

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Hw do you find the domain for $f (x) = \frac{2 x + 7}{x^{2} - 13 x - 30}$ $f(x)= (2x+7)/(x^2-13x-30)$ ?

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Answer 1 · 2015-04-15T12:46:43

$f (x) = \frac{2 x + 7}{x^{2} - 13 x - 30}$ $f(x)=(2x+7)/(x^2-13x-30)$
is equivalent to
$f (x) = \frac{2 x + 7}{(x - 15) (x + 2)}$ $f(x) = (2x+7)/((x-15)(x+2))$
which is defined for all values of $x$ $x$ for which the denominator is not $0$ $0$
that is for all values of $x$ $x$ except $x = 15$ $x=15$ and $x = - 2$ $x=-2$

The Domain of $f (x)$ $f(x)$
$= CC - {-2,15}$
(replace $CC$ with $RR$ if you are restricted to Real numbers).

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Hw do you find the domain for $f (x) = \frac{2 x + 7}{x^{2} - 13 x - 30}$ $f(x)= (2x+7)/(x^2-13x-30)$ ?

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Hw do you find the domain for f(x)= (2x+7)/(x^2-13x-30)f(x)=2x+7x2−13x−30f(x)= (2x+7)/(x^2-13x-30)?

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Hw do you find the domain for $f (x) = \frac{2 x + 7}{x^{2} - 13 x - 30}$ $f(x)= (2x+7)/(x^2-13x-30)$ ?