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Finding the domain of a function worksheets Grade 10

Find the domain of functions with denominators and square roots.

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How to do it

The domain is every x you are allowed to use. A denominator cannot be 0, and what is under a square root must be 0 or more. Write x ≠ 3 or x ≥ 3.

f(x)=x+3x−1domain: x≠1f(x) = \dfrac{x + 3}{x - 1}\quad \text{domain: }x \ne 1
x−1=0 when x=1x - 1 = 0\ \text{when }x = 1the denominator cannot be 0

Example problems

  1. f(x)=x+5x2−2x−15domain: f(x) = \dfrac{x + 5}{x^{2} - 2x - 15}\quad \text{domain: }
  2. f(x)=4x−12domain: f(x) = \sqrt{4x - 12}\quad \text{domain: }
  3. f(x)=x+5x2+9x+18domain: f(x) = \dfrac{x + 5}{x^{2} + 9x + 18}\quad \text{domain: }
  4. f(x)=x+2x+6domain: f(x) = \dfrac{x + 2}{x + 6}\quad \text{domain: }

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change