- Difficulty
- Introductory
- Suggested time
- 2 min
- Marks
- 1
Functions, graphs and inverses practice question 2
Find the largest value of in the domain of the function below.
Two things can go wrong: a square root of a negative number, and a division by zero. Deal with the square root first.
The square root needs . Solve that for , then check whether the denominator rules out anything at that end.
A number, as a fraction or a decimal.
Theory UBC Math 100 §1.5CLP-1 §0.4Key results
Worked solution
Strategy
The domain is every x for which the formula makes sense. The square root needs a non-negative argument and the denominator must not be zero; the largest allowed x comes from the square root.
Working
The square root is defined only for a non-negative argument.
The denominator excludes one more point, well to the left.
The right-hand end is included: at x = 7/2 the square root is 0, which is allowed.
Answer
The answer is seven halves, or 3.5.
Check
g(3.5) = √0/6.5 = 0 is defined, while at x = 3.6 the root would be √(−0.2), which is not.
Where this goes wrong
Excluding 7/2 because “the square root of zero is a problem”. Zero under a square root is fine; zero in a denominator is not, and the denominator is x + 3, not the root.
Try a similar question
Let . Find the domain of , show that is odd, and find a formula for .Saved in this browser only.