Find Where Undefined/Discontinuous f(x)=(x-3)/(x^2+3x-18)

$f (x) = \frac{x - 3}{x^{2} + 3 x - 18}$

Step 1

Set the denominator in $\frac{x - 3}{x^{2} + 3 x - 18}$ equal to $0$ to find where the expression is undefined.

$x^{2} + 3 x - 18 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} + 3 x - 18$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $3$ .

$- 3, 6$

Write the factored form using these integers.

$(x - 3) (x + 6) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 3 = 0$

$x + 6 = 0$

Set $x - 3$ equal to $0$ and solve for $x$ .

Set $x - 3$ equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $(x - 3) (x + 6) = 0$ true.

$x = 3, - 6$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = - 6, x = 3$

Step 4

Find Where Undefined/Discontinuous f(x)=(x-3)/(x^2+3x-18)

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