Finite Math Examples

Find the Domain and Range f(x) = square root of 6-7x
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
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Step 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 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Dividing two negative values results in a positive value.
Step 3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 4
The range is the set of all valid values. Use the graph to find the range.
Interval Notation:
Set-Builder Notation:
Step 5
Determine the domain and range.
Domain:
Range:
Step 6