Find the restrictions first, then write the domain
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Video lessonDomains of functions: three common restrictions
Video coming soonFour rule cards
Polynomials
Usually defined for all real numbers.
Usually defined for all real numbers.
Fractions
The denominator cannot equal 0.
The denominator cannot equal 0.
Even-degree radicals
The radicand must be greater than or equal to 0.
The radicand must be greater than or equal to 0.
Logarithms
The argument must be greater than 0.
The argument must be greater than 0.
Worked example
Find the domain of $f(x) = \sqrt{2x - 1}$.
Write out the restriction yourself first, then read the solution.
Show solution
From $2x - 1 \geq 0$ we get $x \geq 1/2$, so the domain is $[1/2, +\infty)$.