Finite Math Examples

Determine if Continuous g(x)=((x)^(42x^4-x^3+x^2-x+8))/(x^2-5x-14)
Step 1
Find the domain to determine if the expression is continuous.
Tap for more steps...
Step 1.1
Set the denominator in equal to to find where the expression is undefined.
Step 1.2
Solve for .
Tap for more steps...
Step 1.2.1
Factor using the AC method.
Tap for more steps...
Step 1.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 1.2.1.2
Write the factored form using these integers.
Step 1.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 1.2.3
Set equal to and solve for .
Tap for more steps...
Step 1.2.3.1
Set equal to .
Step 1.2.3.2
Add to both sides of the equation.
Step 1.2.4
Set equal to and solve for .
Tap for more steps...
Step 1.2.4.1
Set equal to .
Step 1.2.4.2
Subtract from both sides of the equation.
Step 1.2.5
The final solution is all the values that make true.
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
Since the domain is not all real numbers, is not continuous over all real numbers.
Not continuous
Step 3