Finite Math Examples

Determine if Continuous f(x) = square root of 14-3x
Step 1
Find the domain to determine if the expression is continuous.
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Step 1.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2
Solve for .
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Step 1.2.1
Subtract from both sides of the inequality.
Step 1.2.2
Divide each term in by and simplify.
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Step 1.2.2.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Step 1.2.2.2
Simplify the left side.
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Step 1.2.2.2.1
Cancel the common factor of .
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Step 1.2.2.2.1.1
Cancel the common factor.
Step 1.2.2.2.1.2
Divide by .
Step 1.2.2.3
Simplify the right side.
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Step 1.2.2.3.1
Dividing two negative values results in a positive value.
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
The expression is continuous.
Continuous
Step 3