Find Where Undefined/Discontinuous f(x)=(2x+14)/(x^2+9x+14)

$f (x) = \frac{2 x + 14}{x^{2} + 9 x + 14}$

Step 1

Set the denominator in $\frac{2 x + 14}{x^{2} + 9 x + 14}$ equal to $0$ to find where the expression is undefined.

$x^{2} + 9 x + 14 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} + 9 x + 14$ 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 $14$ and whose sum is $9$ .

$2, 7$

Write the factored form using these integers.

$(x + 2) (x + 7) = 0$

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

$x + 2 = 0$

$x + 7 = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Set $x + 7$ equal to $0$ and solve for $x$ .

Set $x + 7$ equal to $0$ .

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

The final solution is all the values that make $(x + 2) (x + 7) = 0$ true.

$x = - 2, - 7$

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 $0$ .

$x = - 7, x = - 2$

Step 4

Find Where Undefined/Discontinuous f(x)=(2x+14)/(x^2+9x+14)

Related Questions

Support LCMGCF.com by disabling your adblocker.